Analysis notes

  • Updated 4/23 with new weights, only included Stage 2 results, and harmonized y-axis
  • Reference timepoint is fixed at 158 days for Stage 1, and 124 days for Stage 2, which is the minimum timepoint for the latest COVID-19 endpoint across both vaccine and placebo arms.
  • Adjusted for standardized_risk_score.
  • Showing estimates with pointwise confidence intervals. Both raw results and results assuming monotonicity are shown. For the VE scaled graphs, only included graphs assuming monotonicity.
  • CIs for risk in graphs are bounded between 0 and 1. CIs for VE in graphs are bounded above by 1.

Stage 2

IgG Spike Index

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.32 2100 0.00522 0.00105 3.17e-03 0.00727
3.42 2650 0.00594 0.00134 3.32e-03 0.00855
3.52 3340 0.00594 0.00134 3.32e-03 0.00855
3.62 4200 0.00594 0.00134 3.32e-03 0.00855
3.72 5290 0.00599 0.00136 3.33e-03 0.00865
3.82 6660 0.00599 0.00136 3.33e-03 0.00866
3.92 8380 0.00600 0.00136 3.33e-03 0.00866
4.02 10500 0.00606 0.00139 3.34e-03 0.00878
4.12 13300 0.00606 0.00139 3.34e-03 0.00878
4.22 16700 0.00609 0.00138 3.39e-03 0.00880
4.32 21000 0.00609 0.00138 3.39e-03 0.00880
4.42 26500 0.00609 0.00138 3.39e-03 0.00879
4.52 33400 0.00619 0.00139 3.46e-03 0.00892
4.62 42000 0.00631 0.00143 3.51e-03 0.00911
4.72 52900 0.00633 0.00143 3.53e-03 0.00913
4.82 66600 0.00634 0.00144 3.53e-03 0.00916
4.92 83800 0.00679 0.00155 3.74e-03 0.00983
5.02 105000 0.00657 0.00153 3.57e-03 0.00957
5.12 133000 0.00669 0.00160 3.56e-03 0.00983
5.22 167000 0.00724 0.00180 3.72e-03 0.01080
5.32 210000 0.00641 0.00186 2.77e-03 0.01000
5.42 265000 0.00567 0.00193 1.89e-03 0.00946
5.52 334000 0.00588 0.00206 1.85e-03 0.00991
5.62 420000 0.00294 0.00145 9.26e-05 0.00578
5.72 529000 0.00243 0.00157 -6.56e-04 0.00551

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.32 2100 0.0000 0.00619 0.00105 4.14e-03 0.00824
3.42 2650 0.0117 0.00619 0.00134 3.57e-03 0.00881
3.52 3340 0.0117 0.00619 0.00134 3.57e-03 0.00881
3.62 4200 0.0117 0.00619 0.00134 3.57e-03 0.00881
3.72 5290 0.0175 0.00619 0.00136 3.53e-03 0.00885
3.82 6660 0.0180 0.00619 0.00136 3.52e-03 0.00885
3.92 8380 0.0186 0.00619 0.00136 3.52e-03 0.00885
4.02 10500 0.0244 0.00619 0.00139 3.47e-03 0.00891
4.12 13300 0.0244 0.00619 0.00139 3.47e-03 0.00891
4.22 16700 0.0371 0.00619 0.00138 3.48e-03 0.00889
4.32 21000 0.0371 0.00619 0.00138 3.48e-03 0.00889
4.42 26500 0.0377 0.00619 0.00138 3.49e-03 0.00889
4.52 33400 0.0542 0.00619 0.00139 3.46e-03 0.00892
4.62 42000 0.0738 0.00619 0.00143 3.39e-03 0.00898
4.72 52900 0.0802 0.00619 0.00143 3.38e-03 0.00899
4.82 66600 0.0818 0.00619 0.00144 3.37e-03 0.00900
4.92 83800 0.1550 0.00619 0.00155 3.14e-03 0.00923
5.02 105000 0.1700 0.00619 0.00153 3.19e-03 0.00919
5.12 133000 0.2090 0.00619 0.00160 3.05e-03 0.00933
5.22 167000 0.2660 0.00619 0.00180 2.67e-03 0.00971
5.32 210000 0.3650 0.00619 0.00186 2.55e-03 0.00983
5.42 265000 0.4840 0.00577 0.00193 1.99e-03 0.00955
5.52 334000 0.6300 0.00577 0.00206 1.74e-03 0.00980
5.62 420000 0.7200 0.00294 0.00145 9.26e-05 0.00578
5.72 529000 0.8660 0.00243 0.00157 -6.56e-04 0.00551

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.32 2100 0.314 0.157 0.00595 0.622
3.42 2650 0.314 0.182 -0.04310 0.671
3.52 3340 0.314 0.182 -0.04310 0.671
3.62 4200 0.314 0.182 -0.04310 0.671
3.72 5290 0.314 0.184 -0.04680 0.674
3.82 6660 0.314 0.184 -0.04720 0.675
3.92 8380 0.314 0.184 -0.04750 0.675
4.02 10500 0.314 0.187 -0.05240 0.680
4.12 13300 0.314 0.187 -0.05240 0.680
4.22 16700 0.314 0.186 -0.05100 0.679
4.32 21000 0.314 0.186 -0.05100 0.679
4.42 26500 0.314 0.186 -0.05080 0.678
4.52 33400 0.314 0.187 -0.05330 0.681
4.62 42000 0.314 0.190 -0.05940 0.687
4.72 52900 0.314 0.191 -0.06010 0.688
4.82 66600 0.314 0.191 -0.06090 0.689
4.92 83800 0.314 0.202 -0.08260 0.710
5.02 105000 0.314 0.200 -0.07830 0.706
5.12 133000 0.314 0.207 -0.09140 0.719
5.22 167000 0.314 0.226 -0.12800 0.756
5.32 210000 0.314 0.232 -0.14000 0.768
5.42 265000 0.360 0.236 -0.10200 0.822
5.52 334000 0.360 0.249 -0.12700 0.847
5.62 420000 0.674 0.169 0.34400 1.000
5.72 529000 0.731 0.179 0.37900 1.080

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.001390 0.006290 0.01170
2.5 317 0.00952 0.001960 0.005670 0.01340
2.6 399 0.00952 0.001960 0.005670 0.01340
2.7 503 0.00952 0.001960 0.005670 0.01340
2.8 633 0.00924 0.001930 0.005470 0.01300
2.9 796 0.00925 0.001930 0.005470 0.01300
3.0 1000 0.00932 0.001940 0.005510 0.01310
3.1 1260 0.00949 0.001980 0.005610 0.01340
3.2 1590 0.00894 0.001910 0.005200 0.01270
3.3 2000 0.00867 0.001870 0.004990 0.01230
3.4 2520 0.00833 0.001860 0.004690 0.01200
3.5 3170 0.00814 0.001840 0.004530 0.01180
3.6 3990 0.00822 0.001860 0.004570 0.01190
3.7 5030 0.00706 0.001700 0.003730 0.01040
3.8 6330 0.00660 0.001640 0.003380 0.00981
3.9 7960 0.00582 0.001580 0.002730 0.00891
4.0 10000 0.00597 0.001630 0.002780 0.00917
4.1 12600 0.00449 0.001410 0.001730 0.00725
4.2 15900 0.00416 0.001430 0.001350 0.00696
4.3 20000 0.00371 0.001340 0.001090 0.00633
4.4 25200 0.00314 0.001270 0.000653 0.00563
4.5 31700 0.00263 0.001140 0.000389 0.00486
4.6 39900 0.00284 0.001250 0.000383 0.00529
4.7 50300 0.00209 0.001160 -0.000188 0.00436
4.8 63300 0.00149 0.000941 -0.000357 0.00333

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00939 0.001390 0.006660 0.01210
2.5 317 0.0153 0.00939 0.001960 0.005540 0.01320
2.6 399 0.0153 0.00939 0.001960 0.005540 0.01320
2.7 503 0.0153 0.00939 0.001960 0.005540 0.01320
2.8 633 0.0161 0.00932 0.001930 0.005550 0.01310
2.9 796 0.0166 0.00932 0.001930 0.005550 0.01310
3.0 1000 0.0216 0.00932 0.001940 0.005520 0.01310
3.1 1260 0.0488 0.00932 0.001980 0.005440 0.01320
3.2 1590 0.0518 0.00894 0.001910 0.005200 0.01270
3.3 2000 0.0546 0.00867 0.001870 0.004990 0.01230
3.4 2520 0.0884 0.00833 0.001860 0.004690 0.01200
3.5 3170 0.1130 0.00818 0.001840 0.004570 0.01180
3.6 3990 0.1190 0.00818 0.001860 0.004530 0.01180
3.7 5030 0.1220 0.00706 0.001700 0.003730 0.01040
3.8 6330 0.1740 0.00660 0.001640 0.003380 0.00981
3.9 7960 0.2180 0.00590 0.001580 0.002800 0.00899
4.0 10000 0.2460 0.00590 0.001630 0.002700 0.00909
4.1 12600 0.3120 0.00449 0.001410 0.001730 0.00725
4.2 15900 0.3770 0.00416 0.001430 0.001350 0.00696
4.3 20000 0.4060 0.00371 0.001340 0.001090 0.00633
4.4 25200 0.4490 0.00314 0.001270 0.000653 0.00563
4.5 31700 0.4770 0.00273 0.001140 0.000494 0.00497
4.6 39900 0.5440 0.00273 0.001250 0.000277 0.00519
4.7 50300 0.5930 0.00209 0.001160 -0.000188 0.00436
4.8 63300 0.6110 0.00149 0.000941 -0.000357 0.00333

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0300 0.093 0.00584 0.00131 0.003280 0.00841
-0.9320 0.117 0.00592 0.00133 0.003310 0.00852
-0.8320 0.147 0.00592 0.00133 0.003310 0.00852
-0.7320 0.186 0.00592 0.00133 0.003310 0.00852
-0.6320 0.234 0.00592 0.00133 0.003310 0.00852
-0.5320 0.294 0.00599 0.00136 0.003320 0.00866
-0.4320 0.370 0.00603 0.00138 0.003330 0.00874
-0.3320 0.466 0.00608 0.00137 0.003390 0.00876
-0.2320 0.587 0.00608 0.00137 0.003390 0.00876
-0.1320 0.739 0.00622 0.00141 0.003450 0.00899
-0.0315 0.930 0.00622 0.00141 0.003450 0.00899
0.0685 1.170 0.00605 0.00140 0.003300 0.00880
0.1680 1.470 0.00584 0.00137 0.003140 0.00853
0.2680 1.860 0.00597 0.00142 0.003190 0.00875
0.3680 2.340 0.00607 0.00145 0.003220 0.00891
0.4680 2.940 0.00616 0.00147 0.003270 0.00905
0.5680 3.700 0.00615 0.00152 0.003180 0.00913
0.6680 4.660 0.00683 0.00180 0.003310 0.01040
0.7680 5.870 0.00736 0.00206 0.003330 0.01140
0.8680 7.390 0.00758 0.00206 0.003550 0.01160
0.9680 9.300 0.00832 0.00224 0.003920 0.01270
1.0700 11.700 0.00790 0.00217 0.003650 0.01220
1.1700 14.700 0.00738 0.00207 0.003320 0.01140
1.2700 18.600 0.00953 0.00297 0.003710 0.01530
1.3700 23.400 0.00827 0.00257 0.003230 0.01330
1.4700 29.400 0.00821 0.00278 0.002760 0.01370
1.5700 37.000 0.00726 0.00264 0.002090 0.01240
1.6700 46.600 0.00694 0.00283 0.001380 0.01250
1.7700 58.700 0.00775 0.00340 0.001090 0.01440
1.8700 73.900 0.00791 0.00365 0.000755 0.01510
1.9700 93.000 0.00865 0.00413 0.000566 0.01670
2.0700 117.000 0.01160 0.00573 0.000404 0.02290
2.1700 147.000 0.01030 0.00749 -0.004340 0.02500

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.0300 0.093 0.00000 0.00662 0.00131 4.05e-03 0.00918
-0.9320 0.117 0.00692 0.00662 0.00133 4.01e-03 0.00922
-0.8320 0.147 0.00692 0.00662 0.00133 4.01e-03 0.00922
-0.7320 0.186 0.00692 0.00662 0.00133 4.01e-03 0.00922
-0.6320 0.234 0.00692 0.00662 0.00133 4.01e-03 0.00922
-0.5320 0.294 0.01380 0.00662 0.00136 3.95e-03 0.00929
-0.4320 0.370 0.01970 0.00662 0.00138 3.91e-03 0.00932
-0.3320 0.466 0.03510 0.00662 0.00137 3.93e-03 0.00930
-0.2320 0.587 0.03560 0.00662 0.00137 3.93e-03 0.00930
-0.1320 0.739 0.06170 0.00662 0.00141 3.84e-03 0.00939
-0.0315 0.930 0.06230 0.00662 0.00141 3.84e-03 0.00939
0.0685 1.170 0.08610 0.00662 0.00140 3.87e-03 0.00936
0.1680 1.470 0.09910 0.00662 0.00137 3.92e-03 0.00931
0.2680 1.860 0.11900 0.00662 0.00142 3.84e-03 0.00939
0.3680 2.340 0.13300 0.00662 0.00145 3.77e-03 0.00946
0.4680 2.940 0.15300 0.00662 0.00147 3.73e-03 0.00951
0.5680 3.700 0.19200 0.00662 0.00152 3.64e-03 0.00959
0.6680 4.660 0.24300 0.00662 0.00180 3.09e-03 0.01010
0.7680 5.870 0.28300 0.00662 0.00206 2.59e-03 0.01060
0.8680 7.390 0.32700 0.00662 0.00206 2.58e-03 0.01060
0.9680 9.300 0.34400 0.00662 0.00224 2.22e-03 0.01100
1.0700 11.700 0.35100 0.00662 0.00217 2.37e-03 0.01090
1.1700 14.700 0.40300 0.00662 0.00207 2.55e-03 0.01070
1.2700 18.600 0.47200 0.00662 0.00297 8.01e-04 0.01240
1.3700 23.400 0.50500 0.00662 0.00257 1.57e-03 0.01170
1.4700 29.400 0.59000 0.00662 0.00278 1.16e-03 0.01210
1.5700 37.000 0.61500 0.00662 0.00264 1.44e-03 0.01180
1.6700 46.600 0.65600 0.00662 0.00283 1.06e-03 0.01220
1.7700 58.700 0.71500 0.00662 0.00340 -5.07e-05 0.01330
1.8700 73.900 0.76200 0.00662 0.00365 -5.38e-04 0.01380
1.9700 93.000 0.79900 0.00662 0.00413 -1.47e-03 0.01470
2.0700 117.000 0.83000 0.00662 0.00573 -4.61e-03 0.01780
2.1700 147.000 0.90000 0.00662 0.00749 -8.06e-03 0.02130

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0300 0.093 0.266 0.180 -0.0862 0.619
-0.9320 0.117 0.266 0.183 -0.0921 0.625
-0.8320 0.147 0.266 0.183 -0.0921 0.625
-0.7320 0.186 0.266 0.183 -0.0921 0.625
-0.6320 0.234 0.266 0.183 -0.0921 0.625
-0.5320 0.294 0.266 0.187 -0.1010 0.634
-0.4320 0.370 0.266 0.190 -0.1050 0.638
-0.3320 0.466 0.266 0.188 -0.1030 0.636
-0.2320 0.587 0.266 0.188 -0.1030 0.635
-0.1320 0.739 0.266 0.195 -0.1150 0.648
-0.0315 0.930 0.266 0.195 -0.1150 0.648
0.0685 1.170 0.266 0.193 -0.1110 0.644
0.1680 1.470 0.266 0.189 -0.1040 0.636
0.2680 1.860 0.266 0.195 -0.1160 0.648
0.3680 2.340 0.266 0.199 -0.1250 0.657
0.4680 2.940 0.266 0.203 -0.1310 0.664
0.5680 3.700 0.266 0.209 -0.1430 0.675
0.6680 4.660 0.266 0.247 -0.2180 0.751
0.7680 5.870 0.266 0.283 -0.2880 0.820
0.8680 7.390 0.266 0.283 -0.2880 0.821
0.9680 9.300 0.266 0.309 -0.3390 0.871
1.0700 11.700 0.266 0.298 -0.3180 0.851
1.1700 14.700 0.266 0.285 -0.2930 0.825
1.2700 18.600 0.266 0.408 -0.5330 1.070
1.3700 23.400 0.266 0.354 -0.4280 0.960
1.4700 29.400 0.266 0.383 -0.4840 1.020
1.5700 37.000 0.266 0.363 -0.4460 0.979
1.6700 46.600 0.266 0.390 -0.4970 1.030
1.7700 58.700 0.266 0.468 -0.6510 1.180
1.8700 73.900 0.266 0.502 -0.7180 1.250
1.9700 93.000 0.266 0.568 -0.8460 1.380
2.0700 117.000 0.266 0.788 -1.2800 1.810
2.1700 147.000 0.266 1.030 -1.7500 2.280

IgG Spike Beta

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.15 1400 0.00522 0.00105 0.003170 0.00727
3.25 1760 0.00594 0.00134 0.003320 0.00855
3.35 2210 0.00594 0.00134 0.003320 0.00855
3.45 2790 0.00594 0.00134 0.003320 0.00855
3.55 3510 0.00594 0.00134 0.003320 0.00855
3.65 4420 0.00599 0.00136 0.003330 0.00865
3.75 5560 0.00599 0.00136 0.003330 0.00866
3.85 7000 0.00599 0.00136 0.003330 0.00866
3.95 8810 0.00601 0.00136 0.003360 0.00867
4.05 11100 0.00610 0.00139 0.003370 0.00882
4.15 14000 0.00617 0.00142 0.003380 0.00896
4.25 17600 0.00626 0.00145 0.003420 0.00911
4.35 22100 0.00630 0.00145 0.003460 0.00915
4.45 27900 0.00630 0.00145 0.003470 0.00914
4.55 35100 0.00635 0.00143 0.003540 0.00916
4.65 44200 0.00643 0.00145 0.003590 0.00928
4.75 55600 0.00657 0.00149 0.003660 0.00949
4.85 70000 0.00708 0.00163 0.003890 0.01030
4.95 88100 0.00687 0.00161 0.003720 0.01000
5.05 111000 0.00706 0.00167 0.003790 0.01030
5.15 140000 0.00733 0.00183 0.003740 0.01090
5.25 176000 0.00603 0.00170 0.002700 0.00937
5.35 221000 0.00712 0.00217 0.002880 0.01140
5.45 279000 0.00523 0.00189 0.001520 0.00893
5.55 351000 0.00467 0.00221 0.000337 0.00900
5.65 442000 0.00211 0.00129 -0.000428 0.00464

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.15 1400 0.0000 0.00628 0.00105 0.004230 0.00833
3.25 1760 0.0117 0.00628 0.00134 0.003660 0.00889
3.35 2210 0.0117 0.00628 0.00134 0.003660 0.00889
3.45 2790 0.0117 0.00628 0.00134 0.003660 0.00889
3.55 3510 0.0117 0.00628 0.00134 0.003660 0.00889
3.65 4420 0.0175 0.00628 0.00136 0.003620 0.00893
3.75 5560 0.0180 0.00628 0.00136 0.003610 0.00894
3.85 7000 0.0180 0.00628 0.00136 0.003610 0.00894
3.95 8810 0.0255 0.00628 0.00136 0.003620 0.00894
4.05 11100 0.0324 0.00628 0.00139 0.003550 0.00900
4.15 14000 0.0393 0.00628 0.00142 0.003490 0.00906
4.25 17600 0.0515 0.00628 0.00145 0.003430 0.00912
4.35 22100 0.0637 0.00628 0.00145 0.003430 0.00912
4.45 27900 0.0648 0.00628 0.00145 0.003440 0.00912
4.55 35100 0.0865 0.00628 0.00143 0.003470 0.00909
4.65 44200 0.1050 0.00628 0.00145 0.003430 0.00912
4.75 55600 0.1310 0.00628 0.00149 0.003360 0.00919
4.85 70000 0.1770 0.00628 0.00163 0.003090 0.00947
4.95 88100 0.1910 0.00628 0.00161 0.003130 0.00942
5.05 111000 0.2110 0.00628 0.00167 0.003010 0.00955
5.15 140000 0.2690 0.00628 0.00183 0.002690 0.00987
5.25 176000 0.3230 0.00628 0.00170 0.002940 0.00961
5.35 221000 0.5070 0.00628 0.00217 0.002030 0.01050
5.45 279000 0.6150 0.00523 0.00189 0.001520 0.00893
5.55 351000 0.6950 0.00467 0.00221 0.000337 0.00900
5.65 442000 0.8090 0.00211 0.00129 -0.000428 0.00464

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.15 1400 0.304 0.158 -0.00589 0.614
3.25 1760 0.304 0.183 -0.05460 0.663
3.35 2210 0.304 0.183 -0.05460 0.663
3.45 2790 0.304 0.183 -0.05460 0.663
3.55 3510 0.304 0.183 -0.05460 0.663
3.65 4420 0.304 0.185 -0.05830 0.666
3.75 5560 0.304 0.185 -0.05870 0.667
3.85 7000 0.304 0.185 -0.05870 0.667
3.95 8810 0.304 0.185 -0.05840 0.666
4.05 11100 0.304 0.188 -0.06400 0.672
4.15 14000 0.304 0.191 -0.07010 0.678
4.25 17600 0.304 0.194 -0.07550 0.683
4.35 22100 0.304 0.193 -0.07510 0.683
4.45 27900 0.304 0.193 -0.07480 0.683
4.55 35100 0.304 0.192 -0.07220 0.680
4.65 44200 0.304 0.194 -0.07550 0.683
4.75 55600 0.304 0.197 -0.08200 0.690
4.85 70000 0.304 0.210 -0.10800 0.716
4.95 88100 0.304 0.208 -0.10400 0.712
5.05 111000 0.304 0.214 -0.11500 0.723
5.15 140000 0.304 0.230 -0.14600 0.754
5.25 176000 0.304 0.217 -0.12200 0.730
5.35 221000 0.304 0.263 -0.21200 0.820
5.45 279000 0.421 0.228 -0.02640 0.867
5.55 351000 0.482 0.258 -0.02270 0.988
5.65 442000 0.766 0.148 0.47700 1.060

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 0.006290 0.01170
2.5 317 0.00918 0.00192 0.005420 0.01290
2.6 399 0.00918 0.00192 0.005420 0.01290
2.7 503 0.00918 0.00192 0.005420 0.01290
2.8 633 0.00918 0.00192 0.005420 0.01290
2.9 796 0.00918 0.00192 0.005430 0.01290
3.0 1000 0.00923 0.00194 0.005440 0.01300
3.1 1260 0.00894 0.00191 0.005200 0.01270
3.2 1590 0.00867 0.00187 0.005000 0.01230
3.3 2000 0.00784 0.00176 0.004380 0.01130
3.4 2520 0.00805 0.00182 0.004480 0.01160
3.5 3170 0.00755 0.00176 0.004100 0.01100
3.6 3990 0.00684 0.00167 0.003560 0.01010
3.7 5030 0.00717 0.00175 0.003730 0.01060
3.8 6330 0.00710 0.00178 0.003620 0.01060
3.9 7960 0.00488 0.00144 0.002060 0.00770
4.0 10000 0.00418 0.00135 0.001540 0.00682
4.1 12600 0.00464 0.00153 0.001650 0.00763
4.2 15900 0.00355 0.00135 0.000909 0.00620
4.3 20000 0.00318 0.00129 0.000657 0.00571
4.4 25200 0.00228 0.00110 0.000129 0.00443
4.5 31700 0.00185 0.00100 -0.000112 0.00381
4.6 39900 0.00196 0.00110 -0.000195 0.00411

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.00000 0.00916 0.00139 6.43e-03 0.01190
2.5 317 0.00330 0.00916 0.00192 5.41e-03 0.01290
2.6 399 0.00330 0.00916 0.00192 5.41e-03 0.01290
2.7 503 0.00330 0.00916 0.00192 5.41e-03 0.01290
2.8 633 0.00330 0.00916 0.00192 5.41e-03 0.01290
2.9 796 0.00380 0.00916 0.00192 5.41e-03 0.01290
3.0 1000 0.00928 0.00916 0.00194 5.36e-03 0.01300
3.1 1260 0.04980 0.00894 0.00191 5.20e-03 0.01270
3.2 1590 0.05260 0.00867 0.00187 5.00e-03 0.01230
3.3 2000 0.06100 0.00794 0.00176 4.49e-03 0.01140
3.4 2520 0.09200 0.00794 0.00182 4.37e-03 0.01150
3.5 3170 0.10200 0.00755 0.00176 4.10e-03 0.01100
3.6 3990 0.14600 0.00704 0.00167 3.76e-03 0.01030
3.7 5030 0.18500 0.00704 0.00175 3.60e-03 0.01050
3.8 6330 0.20900 0.00704 0.00178 3.55e-03 0.01050
3.9 7960 0.23700 0.00488 0.00144 2.06e-03 0.00770
4.0 10000 0.32300 0.00440 0.00135 1.77e-03 0.00704
4.1 12600 0.41900 0.00440 0.00153 1.41e-03 0.00740
4.2 15900 0.44200 0.00355 0.00135 9.09e-04 0.00620
4.3 20000 0.45900 0.00318 0.00129 6.57e-04 0.00571
4.4 25200 0.49700 0.00228 0.00110 1.29e-04 0.00443
4.5 31700 0.54900 0.00190 0.00100 -5.75e-05 0.00386
4.6 39900 0.58700 0.00190 0.00110 -2.49e-04 0.00406

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1500 0.0701 0.00584 0.00131 0.003280 0.00841
-1.0500 0.0882 0.00592 0.00133 0.003310 0.00852
-0.9550 0.1110 0.00592 0.00133 0.003310 0.00852
-0.8550 0.1400 0.00592 0.00133 0.003310 0.00852
-0.7550 0.1760 0.00592 0.00133 0.003310 0.00852
-0.6550 0.2220 0.00599 0.00136 0.003320 0.00866
-0.5550 0.2790 0.00599 0.00136 0.003320 0.00866
-0.4550 0.3510 0.00603 0.00138 0.003330 0.00874
-0.3550 0.4420 0.00606 0.00137 0.003380 0.00875
-0.2550 0.5560 0.00606 0.00137 0.003380 0.00875
-0.1550 0.7010 0.00612 0.00139 0.003400 0.00883
-0.0545 0.8820 0.00619 0.00140 0.003450 0.00894
0.0455 1.1100 0.00622 0.00140 0.003460 0.00897
0.1450 1.4000 0.00577 0.00136 0.003110 0.00842
0.2450 1.7600 0.00583 0.00137 0.003140 0.00852
0.3450 2.2200 0.00595 0.00141 0.003190 0.00871
0.4450 2.7900 0.00581 0.00141 0.003040 0.00858
0.5450 3.5100 0.00603 0.00147 0.003140 0.00892
0.6450 4.4200 0.00635 0.00157 0.003260 0.00943
0.7450 5.5600 0.00680 0.00177 0.003320 0.01030
0.8450 7.0100 0.00734 0.00196 0.003500 0.01120
0.9450 8.8200 0.00717 0.00198 0.003280 0.01110
1.0500 11.1000 0.00708 0.00205 0.003060 0.01110
1.1500 14.0000 0.00801 0.00232 0.003470 0.01260
1.2500 17.6000 0.00772 0.00227 0.003260 0.01220
1.3500 22.2000 0.00759 0.00231 0.003060 0.01210
1.4500 27.9000 0.00732 0.00244 0.002540 0.01210
1.5500 35.1000 0.00525 0.00208 0.001180 0.00932
1.6500 44.2000 0.00576 0.00230 0.001250 0.01030
1.7500 55.6000 0.00581 0.00277 0.000378 0.01120
1.8500 70.1000 0.00632 0.00351 -0.000559 0.01320
1.9500 88.2000 0.00711 0.00536 -0.003400 0.01760
2.0500 111.0000 0.00686 0.00543 -0.003780 0.01750
2.1500 140.0000 0.01220 0.00668 -0.000879 0.02530
2.2500 176.0000 0.01350 0.00763 -0.001490 0.02840

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.1500 0.0701 0.00000 0.00635 0.00131 0.003790 0.00892
-1.0500 0.0882 0.00692 0.00635 0.00133 0.003750 0.00896
-0.9550 0.1110 0.00692 0.00635 0.00133 0.003750 0.00896
-0.8550 0.1400 0.00692 0.00635 0.00133 0.003750 0.00896
-0.7550 0.1760 0.00692 0.00635 0.00133 0.003750 0.00896
-0.6550 0.2220 0.01380 0.00635 0.00136 0.003680 0.00902
-0.5550 0.2790 0.01380 0.00635 0.00136 0.003680 0.00902
-0.4550 0.3510 0.01970 0.00635 0.00138 0.003650 0.00906
-0.3550 0.4420 0.02920 0.00635 0.00137 0.003670 0.00904
-0.2550 0.5560 0.02920 0.00635 0.00137 0.003670 0.00904
-0.1550 0.7010 0.04110 0.00635 0.00139 0.003640 0.00907
-0.0545 0.8820 0.06810 0.00635 0.00140 0.003610 0.00910
0.0455 1.1100 0.07450 0.00635 0.00140 0.003600 0.00911
0.1450 1.4000 0.08760 0.00635 0.00136 0.003700 0.00901
0.2450 1.7600 0.09930 0.00635 0.00137 0.003660 0.00904
0.3450 2.2200 0.12100 0.00635 0.00141 0.003590 0.00912
0.4450 2.7900 0.14900 0.00635 0.00141 0.003580 0.00912
0.5450 3.5100 0.18000 0.00635 0.00147 0.003460 0.00924
0.6450 4.4200 0.22700 0.00635 0.00157 0.003270 0.00944
0.7450 5.5600 0.25000 0.00635 0.00177 0.002880 0.00983
0.8450 7.0100 0.31100 0.00635 0.00196 0.002510 0.01020
0.9450 8.8200 0.32100 0.00635 0.00198 0.002460 0.01020
1.0500 11.1000 0.34800 0.00635 0.00205 0.002330 0.01040
1.1500 14.0000 0.38400 0.00635 0.00232 0.001810 0.01090
1.2500 17.6000 0.39400 0.00635 0.00227 0.001900 0.01080
1.3500 22.2000 0.48200 0.00635 0.00231 0.001820 0.01090
1.4500 27.9000 0.55700 0.00635 0.00244 0.001570 0.01110
1.5500 35.1000 0.57300 0.00635 0.00208 0.002280 0.01040
1.6500 44.2000 0.62200 0.00635 0.00230 0.001840 0.01090
1.7500 55.6000 0.68800 0.00635 0.00277 0.000922 0.01180
1.8500 70.1000 0.75200 0.00635 0.00351 -0.000523 0.01320
1.9500 88.2000 0.78700 0.00635 0.00536 -0.004160 0.01690
2.0500 111.0000 0.84500 0.00635 0.00543 -0.004280 0.01700
2.1500 140.0000 0.89200 0.00635 0.00668 -0.006740 0.01940
2.2500 176.0000 0.91300 0.00635 0.00763 -0.008600 0.02130

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1500 0.0701 0.295 0.177 -0.0523 0.643
-1.0500 0.0882 0.295 0.180 -0.0581 0.649
-0.9550 0.1110 0.295 0.180 -0.0581 0.649
-0.8550 0.1400 0.295 0.180 -0.0581 0.649
-0.7550 0.1760 0.295 0.180 -0.0581 0.649
-0.6550 0.2220 0.295 0.185 -0.0669 0.658
-0.5550 0.2790 0.295 0.185 -0.0669 0.658
-0.4550 0.3510 0.295 0.187 -0.0711 0.662
-0.3550 0.4420 0.295 0.186 -0.0688 0.660
-0.2550 0.5560 0.295 0.186 -0.0688 0.660
-0.1550 0.7010 0.295 0.188 -0.0730 0.664
-0.0545 0.8820 0.295 0.190 -0.0767 0.667
0.0455 1.1100 0.295 0.191 -0.0781 0.669
0.1450 1.4000 0.295 0.184 -0.0652 0.656
0.2450 1.7600 0.295 0.186 -0.0696 0.660
0.3450 2.2200 0.295 0.191 -0.0794 0.670
0.4450 2.7900 0.295 0.192 -0.0803 0.671
0.5450 3.5100 0.295 0.200 -0.0967 0.687
0.6450 4.4200 0.295 0.214 -0.1230 0.714
0.7450 5.5600 0.295 0.240 -0.1760 0.766
0.8450 7.0100 0.295 0.266 -0.2260 0.817
0.9450 8.8200 0.295 0.269 -0.2320 0.823
1.0500 11.1000 0.295 0.279 -0.2510 0.842
1.1500 14.0000 0.295 0.315 -0.3210 0.912
1.2500 17.6000 0.295 0.308 -0.3090 0.900
1.3500 22.2000 0.295 0.314 -0.3190 0.910
1.4500 27.9000 0.295 0.331 -0.3540 0.945
1.5500 35.1000 0.295 0.282 -0.2570 0.848
1.6500 44.2000 0.295 0.312 -0.3170 0.907
1.7500 55.6000 0.295 0.376 -0.4420 1.030
1.8500 70.1000 0.295 0.476 -0.6380 1.230
1.9500 88.2000 0.295 0.727 -1.1300 1.720
2.0500 111.0000 0.295 0.736 -1.1500 1.740
2.1500 140.0000 0.295 0.906 -1.4800 2.070
2.2500 176.0000 0.295 1.030 -1.7300 2.320

IgG Spike Alpha

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.31 2040 0.00522 0.00105 0.003170 0.00727
3.41 2570 0.00594 0.00134 0.003320 0.00855
3.51 3230 0.00594 0.00134 0.003320 0.00855
3.61 4070 0.00594 0.00134 0.003320 0.00855
3.71 5120 0.00599 0.00136 0.003330 0.00865
3.81 6440 0.00599 0.00136 0.003330 0.00866
3.91 8110 0.00600 0.00136 0.003330 0.00866
4.01 10200 0.00600 0.00136 0.003330 0.00866
4.11 12900 0.00607 0.00138 0.003370 0.00878
4.21 16200 0.00609 0.00138 0.003390 0.00880
4.31 20400 0.00613 0.00139 0.003410 0.00886
4.41 25700 0.00621 0.00142 0.003420 0.00899
4.51 32300 0.00631 0.00143 0.003510 0.00911
4.61 40700 0.00634 0.00143 0.003530 0.00914
4.71 51200 0.00634 0.00143 0.003530 0.00916
4.81 64400 0.00661 0.00150 0.003670 0.00955
4.91 81100 0.00657 0.00153 0.003570 0.00957
5.01 102000 0.00688 0.00161 0.003720 0.01000
5.11 129000 0.00691 0.00168 0.003620 0.01020
5.21 162000 0.00661 0.00177 0.003130 0.01010
5.31 204000 0.00599 0.00175 0.002550 0.00943
5.41 257000 0.00475 0.00165 0.001530 0.00798
5.51 323000 0.00609 0.00235 0.001470 0.01070
5.61 407000 0.00262 0.00143 -0.000189 0.00543

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.31 2040 0.0000 0.00619 0.00105 0.004140 0.00824
3.41 2570 0.0117 0.00619 0.00134 0.003570 0.00881
3.51 3230 0.0117 0.00619 0.00134 0.003570 0.00881
3.61 4070 0.0117 0.00619 0.00134 0.003570 0.00881
3.71 5120 0.0175 0.00619 0.00136 0.003530 0.00885
3.81 6440 0.0180 0.00619 0.00136 0.003530 0.00885
3.91 8110 0.0186 0.00619 0.00136 0.003520 0.00886
4.01 10200 0.0186 0.00619 0.00136 0.003520 0.00886
4.11 12900 0.0302 0.00619 0.00138 0.003480 0.00890
4.21 16200 0.0371 0.00619 0.00138 0.003480 0.00889
4.31 20400 0.0404 0.00619 0.00139 0.003460 0.00892
4.41 25700 0.0468 0.00619 0.00142 0.003400 0.00898
4.51 32300 0.0744 0.00619 0.00143 0.003390 0.00898
4.61 40700 0.0813 0.00619 0.00143 0.003380 0.00900
4.71 51200 0.0823 0.00619 0.00143 0.003380 0.00900
4.81 64400 0.1330 0.00619 0.00150 0.003250 0.00913
4.91 81100 0.1700 0.00619 0.00153 0.003190 0.00919
5.01 102000 0.1870 0.00619 0.00161 0.003020 0.00935
5.11 129000 0.2340 0.00619 0.00168 0.002900 0.00948
5.21 162000 0.3110 0.00619 0.00177 0.002710 0.00967
5.31 204000 0.3850 0.00599 0.00175 0.002550 0.00943
5.41 257000 0.5450 0.00537 0.00165 0.002150 0.00860
5.51 323000 0.6820 0.00537 0.00235 0.000760 0.00999
5.61 407000 0.7650 0.00262 0.00143 -0.000189 0.00543

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.31 2040 0.314 0.157 0.00583 0.622
3.41 2570 0.314 0.182 -0.04320 0.671
3.51 3230 0.314 0.182 -0.04320 0.671
3.61 4070 0.314 0.182 -0.04320 0.671
3.71 5120 0.314 0.184 -0.04690 0.674
3.81 6440 0.314 0.184 -0.04730 0.675
3.91 8110 0.314 0.184 -0.04760 0.675
4.01 10200 0.314 0.184 -0.04760 0.675
4.11 12900 0.314 0.186 -0.05130 0.679
4.21 16200 0.314 0.186 -0.05110 0.679
4.31 20400 0.314 0.187 -0.05320 0.681
4.41 25700 0.314 0.190 -0.05870 0.686
4.51 32300 0.314 0.190 -0.05950 0.687
4.61 40700 0.314 0.191 -0.06050 0.688
4.71 51200 0.314 0.191 -0.06090 0.688
4.81 64400 0.314 0.197 -0.07280 0.700
4.91 81100 0.314 0.200 -0.07830 0.706
5.01 102000 0.314 0.208 -0.09400 0.721
5.11 129000 0.314 0.214 -0.10600 0.734
5.21 162000 0.314 0.224 -0.12400 0.752
5.31 204000 0.335 0.220 -0.09560 0.767
5.41 257000 0.404 0.204 0.00359 0.805
5.51 323000 0.404 0.277 -0.13800 0.947
5.61 407000 0.710 0.165 0.38600 1.030

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.001390 0.006290 0.01170
2.5 317 0.00924 0.001930 0.005470 0.01300
2.6 399 0.00924 0.001930 0.005470 0.01300
2.7 503 0.00924 0.001930 0.005470 0.01300
2.8 633 0.00924 0.001930 0.005470 0.01300
2.9 796 0.00924 0.001930 0.005470 0.01300
3.0 1000 0.00930 0.001940 0.005500 0.01310
3.1 1260 0.00949 0.001980 0.005610 0.01340
3.2 1590 0.00920 0.001940 0.005400 0.01300
3.3 2000 0.00894 0.001910 0.005200 0.01270
3.4 2520 0.00842 0.001840 0.004810 0.01200
3.5 3170 0.00794 0.001790 0.004430 0.01150
3.6 3990 0.00789 0.001810 0.004330 0.01140
3.7 5030 0.00713 0.001710 0.003770 0.01050
3.8 6330 0.00683 0.001700 0.003500 0.01020
3.9 7960 0.00637 0.001650 0.003130 0.00961
4.0 10000 0.00622 0.001710 0.002860 0.00958
4.1 12600 0.00425 0.001430 0.001440 0.00706
4.2 15900 0.00424 0.001460 0.001370 0.00711
4.3 20000 0.00311 0.001250 0.000656 0.00557
4.4 25200 0.00257 0.001110 0.000396 0.00474
4.5 31700 0.00281 0.001240 0.000375 0.00524
4.6 39900 0.00244 0.001190 0.000113 0.00477
4.7 50300 0.00147 0.000944 -0.000377 0.00332

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00925 0.001390 0.006520 0.01200
2.5 317 0.0151 0.00925 0.001930 0.005480 0.01300
2.6 399 0.0151 0.00925 0.001930 0.005480 0.01300
2.7 503 0.0151 0.00925 0.001930 0.005480 0.01300
2.8 633 0.0156 0.00925 0.001930 0.005470 0.01300
2.9 796 0.0156 0.00925 0.001930 0.005470 0.01300
3.0 1000 0.0206 0.00925 0.001940 0.005450 0.01310
3.1 1260 0.0488 0.00925 0.001980 0.005370 0.01310
3.2 1590 0.0491 0.00920 0.001940 0.005400 0.01300
3.3 2000 0.0524 0.00894 0.001910 0.005200 0.01270
3.4 2520 0.0604 0.00842 0.001840 0.004810 0.01200
3.5 3170 0.0854 0.00794 0.001790 0.004430 0.01150
3.6 3990 0.1170 0.00789 0.001810 0.004330 0.01140
3.7 5030 0.1460 0.00713 0.001710 0.003770 0.01050
3.8 6330 0.1870 0.00683 0.001700 0.003500 0.01020
3.9 7960 0.1980 0.00637 0.001650 0.003130 0.00961
4.0 10000 0.2730 0.00622 0.001710 0.002860 0.00958
4.1 12600 0.2980 0.00425 0.001430 0.001440 0.00706
4.2 15900 0.3970 0.00424 0.001460 0.001370 0.00711
4.3 20000 0.4410 0.00311 0.001250 0.000656 0.00557
4.4 25200 0.4630 0.00269 0.001110 0.000515 0.00486
4.5 31700 0.5350 0.00269 0.001240 0.000256 0.00512
4.6 39900 0.5530 0.00244 0.001190 0.000113 0.00477
4.7 50300 0.6200 0.00147 0.000944 -0.000377 0.00332

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1200 0.0757 0.00584 0.00131 3.28e-03 0.00841
-1.0200 0.0953 0.00586 0.00131 3.29e-03 0.00843
-0.9210 0.1200 0.00592 0.00133 3.31e-03 0.00852
-0.8210 0.1510 0.00592 0.00133 3.31e-03 0.00852
-0.7210 0.1900 0.00592 0.00133 3.31e-03 0.00852
-0.6210 0.2390 0.00593 0.00134 3.31e-03 0.00855
-0.5210 0.3010 0.00599 0.00136 3.32e-03 0.00866
-0.4210 0.3790 0.00603 0.00138 3.33e-03 0.00874
-0.3210 0.4780 0.00606 0.00137 3.38e-03 0.00875
-0.2210 0.6010 0.00613 0.00139 3.42e-03 0.00885
-0.1210 0.7570 0.00613 0.00139 3.42e-03 0.00885
-0.0209 0.9530 0.00592 0.00136 3.25e-03 0.00858
0.0791 1.2000 0.00602 0.00138 3.30e-03 0.00873
0.1790 1.5100 0.00584 0.00138 3.15e-03 0.00854
0.2790 1.9000 0.00593 0.00140 3.19e-03 0.00867
0.3790 2.3900 0.00612 0.00147 3.25e-03 0.00900
0.4790 3.0100 0.00613 0.00152 3.15e-03 0.00910
0.5790 3.7900 0.00587 0.00148 2.97e-03 0.00876
0.6790 4.7800 0.00696 0.00185 3.34e-03 0.01060
0.7790 6.0100 0.00733 0.00197 3.46e-03 0.01120
0.8790 7.5700 0.00769 0.00210 3.57e-03 0.01180
0.9790 9.5300 0.00770 0.00210 3.58e-03 0.01180
1.0800 12.0000 0.00833 0.00234 3.75e-03 0.01290
1.1800 15.1000 0.00856 0.00252 3.61e-03 0.01350
1.2800 19.0000 0.00883 0.00264 3.65e-03 0.01400
1.3800 23.9000 0.00675 0.00253 1.80e-03 0.01170
1.4800 30.1000 0.00654 0.00244 1.74e-03 0.01130
1.5800 37.9000 0.00631 0.00252 1.36e-03 0.01130
1.6800 47.8000 0.00576 0.00294 -6.90e-06 0.01150
1.7800 60.1000 0.00534 0.00312 -7.68e-04 0.01150
1.8800 75.7000 0.00680 0.00403 -1.10e-03 0.01470
1.9800 95.3000 0.01200 0.00607 8.69e-05 0.02390
2.0800 120.0000 0.01880 0.01040 -1.59e-03 0.03910

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.1200 0.0757 0.00000 0.00646 0.00131 0.003900 0.00902
-1.0200 0.0953 0.00109 0.00646 0.00131 0.003890 0.00903
-0.9210 0.1200 0.00692 0.00646 0.00133 0.003850 0.00907
-0.8210 0.1510 0.00692 0.00646 0.00133 0.003850 0.00907
-0.7210 0.1900 0.00692 0.00646 0.00133 0.003850 0.00907
-0.6210 0.2390 0.00802 0.00646 0.00134 0.003840 0.00908
-0.5210 0.3010 0.01380 0.00646 0.00136 0.003790 0.00913
-0.4210 0.3790 0.01970 0.00646 0.00138 0.003760 0.00916
-0.3210 0.4780 0.02920 0.00646 0.00137 0.003780 0.00914
-0.2210 0.6010 0.04640 0.00646 0.00139 0.003740 0.00918
-0.1210 0.7570 0.04690 0.00646 0.00139 0.003740 0.00918
-0.0209 0.9530 0.06250 0.00646 0.00136 0.003800 0.00912
0.0791 1.2000 0.08720 0.00646 0.00138 0.003750 0.00917
0.1790 1.5100 0.10000 0.00646 0.00138 0.003760 0.00916
0.2790 1.9000 0.11900 0.00646 0.00140 0.003720 0.00920
0.3790 2.3900 0.14500 0.00646 0.00147 0.003590 0.00933
0.4790 3.0100 0.18000 0.00646 0.00152 0.003480 0.00944
0.5790 3.7900 0.19300 0.00646 0.00148 0.003560 0.00936
0.6790 4.7800 0.25400 0.00646 0.00185 0.002840 0.01010
0.7790 6.0100 0.30000 0.00646 0.00197 0.002600 0.01030
0.8790 7.5700 0.33900 0.00646 0.00210 0.002350 0.01060
0.9790 9.5300 0.34000 0.00646 0.00210 0.002340 0.01060
1.0800 12.0000 0.38200 0.00646 0.00234 0.001880 0.01100
1.1800 15.1000 0.44200 0.00646 0.00252 0.001510 0.01140
1.2800 19.0000 0.50300 0.00646 0.00264 0.001280 0.01160
1.3800 23.9000 0.58000 0.00646 0.00253 0.001510 0.01140
1.4800 30.1000 0.61400 0.00646 0.00244 0.001670 0.01130
1.5800 37.9000 0.63800 0.00646 0.00252 0.001510 0.01140
1.6800 47.8000 0.69100 0.00646 0.00294 0.000694 0.01220
1.7800 60.1000 0.76500 0.00646 0.00312 0.000349 0.01260
1.8800 75.7000 0.80100 0.00646 0.00403 -0.001440 0.01440
1.9800 95.3000 0.83200 0.00646 0.00607 -0.005440 0.01840
2.0800 120.0000 0.88400 0.00646 0.01040 -0.013900 0.02680

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1200 0.0757 0.284 0.178 -0.0661 0.633
-1.0200 0.0953 0.284 0.179 -0.0670 0.634
-0.9210 0.1200 0.284 0.181 -0.0719 0.639
-0.8210 0.1510 0.284 0.181 -0.0719 0.639
-0.7210 0.1900 0.284 0.181 -0.0719 0.639
-0.6210 0.2390 0.284 0.182 -0.0737 0.641
-0.5210 0.3010 0.284 0.186 -0.0808 0.648
-0.4210 0.3790 0.284 0.188 -0.0850 0.652
-0.3210 0.4780 0.284 0.187 -0.0827 0.650
-0.2210 0.6010 0.284 0.189 -0.0871 0.654
-0.1210 0.7570 0.284 0.189 -0.0870 0.654
-0.0209 0.9530 0.284 0.185 -0.0794 0.647
0.0791 1.2000 0.284 0.189 -0.0867 0.654
0.1790 1.5100 0.284 0.188 -0.0842 0.651
0.2790 1.9000 0.284 0.191 -0.0902 0.657
0.3790 2.3900 0.284 0.200 -0.1080 0.676
0.4790 3.0100 0.284 0.207 -0.1220 0.689
0.5790 3.7900 0.284 0.202 -0.1120 0.679
0.6790 4.7800 0.284 0.252 -0.2100 0.778
0.7790 6.0100 0.284 0.269 -0.2440 0.811
0.8790 7.5700 0.284 0.286 -0.2780 0.845
0.9790 9.5300 0.284 0.287 -0.2790 0.846
1.0800 12.0000 0.284 0.319 -0.3420 0.909
1.1800 15.1000 0.284 0.344 -0.3910 0.959
1.2800 19.0000 0.284 0.361 -0.4230 0.990
1.3800 23.9000 0.284 0.345 -0.3920 0.959
1.4800 30.1000 0.284 0.334 -0.3700 0.937
1.5800 37.9000 0.284 0.344 -0.3910 0.959
1.6800 47.8000 0.284 0.401 -0.5030 1.070
1.7800 60.1000 0.284 0.425 -0.5500 1.120
1.8800 75.7000 0.284 0.550 -0.7940 1.360
1.9800 95.3000 0.284 0.828 -1.3400 1.910
2.0800 120.0000 0.284 1.420 -2.4900 3.060

IgG Spike Gamma

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.18 1500 0.00522 0.00105 0.003170 0.00727
3.28 1890 0.00594 0.00134 0.003320 0.00855
3.38 2380 0.00594 0.00134 0.003320 0.00855
3.48 3000 0.00594 0.00134 0.003320 0.00855
3.58 3780 0.00599 0.00136 0.003330 0.00865
3.68 4750 0.00599 0.00136 0.003330 0.00866
3.78 5980 0.00600 0.00136 0.003330 0.00866
3.88 7530 0.00606 0.00139 0.003340 0.00878
3.98 9480 0.00608 0.00138 0.003370 0.00878
4.08 11900 0.00611 0.00139 0.003390 0.00883
4.18 15000 0.00611 0.00139 0.003390 0.00883
4.28 18900 0.00619 0.00142 0.003410 0.00898
4.38 23800 0.00630 0.00145 0.003460 0.00914
4.48 30000 0.00631 0.00143 0.003510 0.00911
4.58 37800 0.00633 0.00143 0.003530 0.00913
4.68 47500 0.00634 0.00143 0.003530 0.00916
4.78 59800 0.00680 0.00156 0.003740 0.00986
4.88 75300 0.00677 0.00158 0.003670 0.00987
4.98 94800 0.00700 0.00165 0.003770 0.01020
5.08 119000 0.00726 0.00182 0.003690 0.01080
5.18 150000 0.00626 0.00172 0.002900 0.00963
5.28 189000 0.00542 0.00173 0.002030 0.00881
5.38 238000 0.00485 0.00180 0.001310 0.00838
5.48 300000 0.00569 0.00234 0.001100 0.01030
5.58 378000 0.00265 0.00141 -0.000118 0.00543

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.18 1500 0.0000 0.00622 0.00105 0.004170 0.00827
3.28 1890 0.0117 0.00622 0.00134 0.003600 0.00884
3.38 2380 0.0117 0.00622 0.00134 0.003600 0.00884
3.48 3000 0.0117 0.00622 0.00134 0.003600 0.00884
3.58 3780 0.0175 0.00622 0.00136 0.003560 0.00888
3.68 4750 0.0180 0.00622 0.00136 0.003560 0.00888
3.78 5980 0.0186 0.00622 0.00136 0.003550 0.00889
3.88 7530 0.0249 0.00622 0.00139 0.003500 0.00894
3.98 9480 0.0313 0.00622 0.00138 0.003510 0.00893
4.08 11900 0.0382 0.00622 0.00139 0.003500 0.00894
4.18 15000 0.0382 0.00622 0.00139 0.003500 0.00894
4.28 18900 0.0457 0.00622 0.00142 0.003440 0.00900
4.38 23800 0.0643 0.00622 0.00145 0.003380 0.00906
4.48 30000 0.0744 0.00622 0.00143 0.003420 0.00902
4.58 37800 0.0807 0.00622 0.00143 0.003420 0.00902
4.68 47500 0.0818 0.00622 0.00143 0.003410 0.00903
4.78 59800 0.1260 0.00622 0.00156 0.003160 0.00928
4.88 75300 0.1710 0.00622 0.00158 0.003120 0.00932
4.98 94800 0.2020 0.00622 0.00165 0.002980 0.00946
5.08 119000 0.2580 0.00622 0.00182 0.002650 0.00979
5.18 150000 0.3050 0.00622 0.00172 0.002850 0.00958
5.28 189000 0.4690 0.00542 0.00173 0.002030 0.00881
5.38 238000 0.5950 0.00485 0.00180 0.001310 0.00838
5.48 300000 0.6900 0.00485 0.00234 0.000256 0.00944
5.58 378000 0.7810 0.00265 0.00141 -0.000118 0.00543

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.18 1500 0.310 0.157 0.0017 0.619
3.28 1890 0.310 0.182 -0.0472 0.668
3.38 2380 0.310 0.182 -0.0472 0.668
3.48 3000 0.310 0.182 -0.0472 0.668
3.58 3780 0.310 0.184 -0.0509 0.672
3.68 4750 0.310 0.185 -0.0513 0.672
3.78 5980 0.310 0.185 -0.0517 0.672
3.88 7530 0.310 0.187 -0.0564 0.677
3.98 9480 0.310 0.187 -0.0553 0.676
4.08 11900 0.310 0.187 -0.0563 0.677
4.18 15000 0.310 0.187 -0.0563 0.677
4.28 18900 0.310 0.190 -0.0623 0.683
4.38 23800 0.310 0.193 -0.0673 0.688
4.48 30000 0.310 0.191 -0.0635 0.684
4.58 37800 0.310 0.191 -0.0642 0.685
4.68 47500 0.310 0.191 -0.0649 0.686
4.78 59800 0.310 0.203 -0.0882 0.709
4.88 75300 0.310 0.205 -0.0917 0.712
4.98 94800 0.310 0.212 -0.1050 0.725
5.08 119000 0.310 0.228 -0.1370 0.758
5.18 150000 0.310 0.218 -0.1170 0.738
5.28 189000 0.399 0.213 -0.0191 0.816
5.38 238000 0.463 0.216 0.0384 0.887
5.48 300000 0.463 0.273 -0.0719 0.997
5.58 378000 0.706 0.163 0.3850 1.030

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 0.006290 0.01170
2.5 317 0.00920 0.00192 0.005440 0.01300
2.6 399 0.00920 0.00192 0.005440 0.01300
2.7 503 0.00920 0.00192 0.005440 0.01300
2.8 633 0.00932 0.00194 0.005510 0.01310
2.9 796 0.00921 0.00194 0.005400 0.01300
3.0 1000 0.00923 0.00195 0.005410 0.01300
3.1 1260 0.00895 0.00191 0.005200 0.01270
3.2 1590 0.00861 0.00189 0.004900 0.01230
3.3 2000 0.00832 0.00185 0.004690 0.01200
3.4 2520 0.00846 0.00189 0.004750 0.01220
3.5 3170 0.00795 0.00182 0.004380 0.01150
3.6 3990 0.00652 0.00162 0.003340 0.00971
3.7 5030 0.00649 0.00169 0.003190 0.00979
3.8 6330 0.00632 0.00169 0.003010 0.00963
3.9 7960 0.00565 0.00159 0.002530 0.00876
4.0 10000 0.00420 0.00141 0.001440 0.00695
4.1 12600 0.00427 0.00147 0.001390 0.00715
4.2 15900 0.00357 0.00137 0.000888 0.00624
4.3 20000 0.00332 0.00137 0.000628 0.00601
4.4 25200 0.00285 0.00130 0.000307 0.00539
4.5 31700 0.00189 0.00104 -0.000143 0.00392
4.6 39900 0.00194 0.00105 -0.000124 0.00401

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00919 0.00139 0.006470 0.01190
2.5 317 0.0043 0.00919 0.00192 0.005430 0.01300
2.6 399 0.0043 0.00919 0.00192 0.005430 0.01300
2.7 503 0.0043 0.00919 0.00192 0.005430 0.01300
2.8 633 0.0211 0.00919 0.00194 0.005390 0.01300
2.9 796 0.0496 0.00919 0.00194 0.005380 0.01300
3.0 1000 0.0511 0.00919 0.00195 0.005370 0.01300
3.1 1260 0.0548 0.00895 0.00191 0.005200 0.01270
3.2 1590 0.0861 0.00861 0.00189 0.004900 0.01230
3.3 2000 0.0899 0.00839 0.00185 0.004760 0.01200
3.4 2520 0.1150 0.00839 0.00189 0.004690 0.01210
3.5 3170 0.1390 0.00795 0.00182 0.004380 0.01150
3.6 3990 0.1550 0.00652 0.00162 0.003340 0.00971
3.7 5030 0.2160 0.00649 0.00169 0.003190 0.00979
3.8 6330 0.2580 0.00632 0.00169 0.003010 0.00963
3.9 7960 0.2680 0.00565 0.00159 0.002530 0.00876
4.0 10000 0.3420 0.00423 0.00141 0.001480 0.00699
4.1 12600 0.4220 0.00423 0.00147 0.001350 0.00711
4.2 15900 0.4570 0.00357 0.00137 0.000888 0.00624
4.3 20000 0.4860 0.00332 0.00137 0.000628 0.00601
4.4 25200 0.5130 0.00285 0.00130 0.000307 0.00539
4.5 31700 0.5700 0.00192 0.00104 -0.000117 0.00395
4.6 39900 0.5960 0.00192 0.00105 -0.000150 0.00398

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0500 0.0884 0.00584 0.00131 0.003280 0.00841
-0.9540 0.1110 0.00592 0.00133 0.003310 0.00852
-0.8540 0.1400 0.00592 0.00133 0.003310 0.00852
-0.7540 0.1760 0.00592 0.00133 0.003310 0.00852
-0.6540 0.2220 0.00593 0.00134 0.003310 0.00855
-0.5540 0.2800 0.00603 0.00138 0.003330 0.00874
-0.4540 0.3520 0.00604 0.00138 0.003340 0.00874
-0.3540 0.4430 0.00604 0.00138 0.003340 0.00874
-0.2540 0.5580 0.00608 0.00137 0.003390 0.00876
-0.1540 0.7020 0.00613 0.00139 0.003420 0.00885
-0.0535 0.8840 0.00620 0.00140 0.003450 0.00894
0.0465 1.1100 0.00597 0.00138 0.003270 0.00867
0.1460 1.4000 0.00600 0.00138 0.003290 0.00870
0.2460 1.7600 0.00584 0.00138 0.003140 0.00853
0.3460 2.2200 0.00600 0.00143 0.003200 0.00879
0.4460 2.8000 0.00601 0.00143 0.003210 0.00881
0.5460 3.5200 0.00627 0.00151 0.003320 0.00922
0.6460 4.4300 0.00593 0.00150 0.002980 0.00887
0.7460 5.5800 0.00719 0.00196 0.003350 0.01100
0.8460 7.0200 0.00753 0.00209 0.003440 0.01160
0.9460 8.8400 0.00782 0.00217 0.003560 0.01210
1.0500 11.1000 0.00782 0.00217 0.003570 0.01210
1.1500 14.0000 0.00823 0.00227 0.003780 0.01270
1.2500 17.6000 0.00716 0.00205 0.003140 0.01120
1.3500 22.2000 0.00748 0.00228 0.003010 0.01200
1.4500 28.0000 0.00714 0.00232 0.002590 0.01170
1.5500 35.2000 0.00650 0.00233 0.001940 0.01110
1.6500 44.3000 0.00618 0.00247 0.001330 0.01100
1.7500 55.8000 0.00558 0.00276 0.000165 0.01100
1.8500 70.2000 0.00547 0.00301 -0.000422 0.01140
1.9500 88.4000 0.00500 0.00344 -0.001730 0.01170
2.0500 111.0000 0.00697 0.00354 0.000031 0.01390
2.1500 140.0000 0.00796 0.00416 -0.000193 0.01610

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.0500 0.0884 0.00000 0.00642 0.00131 0.003860 0.00899
-0.9540 0.1110 0.00692 0.00642 0.00133 0.003820 0.00903
-0.8540 0.1400 0.00692 0.00642 0.00133 0.003820 0.00903
-0.7540 0.1760 0.00692 0.00642 0.00133 0.003820 0.00903
-0.6540 0.2220 0.00802 0.00642 0.00134 0.003810 0.00904
-0.5540 0.2800 0.01970 0.00642 0.00138 0.003720 0.00913
-0.4540 0.3520 0.02020 0.00642 0.00138 0.003720 0.00913
-0.3540 0.4430 0.02020 0.00642 0.00138 0.003720 0.00913
-0.2540 0.5580 0.03560 0.00642 0.00137 0.003740 0.00911
-0.1540 0.7020 0.04640 0.00642 0.00139 0.003710 0.00914
-0.0535 0.8840 0.06810 0.00642 0.00140 0.003680 0.00917
0.0465 1.1100 0.07470 0.00642 0.00138 0.003720 0.00913
0.1460 1.4000 0.08130 0.00642 0.00138 0.003720 0.00913
0.2460 1.7600 0.09980 0.00642 0.00138 0.003730 0.00912
0.3460 2.2200 0.12500 0.00642 0.00143 0.003630 0.00922
0.4460 2.8000 0.12700 0.00642 0.00143 0.003620 0.00922
0.5460 3.5200 0.16800 0.00642 0.00151 0.003470 0.00938
0.6460 4.4300 0.19800 0.00642 0.00150 0.003480 0.00937
0.7460 5.5800 0.27400 0.00642 0.00196 0.002590 0.01030
0.8460 7.0200 0.31200 0.00642 0.00209 0.002330 0.01050
0.9460 8.8400 0.34500 0.00642 0.00217 0.002170 0.01070
1.0500 11.1000 0.34700 0.00642 0.00217 0.002180 0.01070
1.1500 14.0000 0.37300 0.00642 0.00227 0.001970 0.01090
1.2500 17.6000 0.42900 0.00642 0.00205 0.002400 0.01040
1.3500 22.2000 0.47700 0.00642 0.00228 0.001950 0.01090
1.4500 28.0000 0.54500 0.00642 0.00232 0.001880 0.01100
1.5500 35.2000 0.58500 0.00642 0.00233 0.001860 0.01100
1.6500 44.3000 0.64200 0.00619 0.00247 0.001340 0.01100
1.7500 55.8000 0.67500 0.00619 0.00276 0.000775 0.01160
1.8500 70.2000 0.73200 0.00619 0.00301 0.000302 0.01210
1.9500 88.4000 0.78000 0.00619 0.00344 -0.000543 0.01290
2.0500 111.0000 0.82000 0.00619 0.00354 -0.000743 0.01310
2.1500 140.0000 0.84100 0.00619 0.00416 -0.001960 0.01430

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0500 0.0884 0.288 0.178 -0.0614 0.637
-0.9540 0.1110 0.288 0.181 -0.0672 0.642
-0.8540 0.1400 0.288 0.181 -0.0672 0.642
-0.7540 0.1760 0.288 0.181 -0.0672 0.642
-0.6540 0.2220 0.288 0.182 -0.0690 0.644
-0.5540 0.2800 0.288 0.188 -0.0802 0.655
-0.4540 0.3520 0.288 0.188 -0.0804 0.656
-0.3540 0.4430 0.288 0.188 -0.0804 0.656
-0.2540 0.5580 0.288 0.186 -0.0779 0.653
-0.1540 0.7020 0.288 0.189 -0.0822 0.657
-0.0535 0.8840 0.288 0.191 -0.0864 0.661
0.0465 1.1100 0.288 0.188 -0.0802 0.655
0.1460 1.4000 0.288 0.188 -0.0813 0.656
0.2460 1.7600 0.288 0.187 -0.0799 0.655
0.3460 2.2200 0.288 0.194 -0.0928 0.668
0.4460 2.8000 0.288 0.195 -0.0937 0.669
0.5460 3.5200 0.288 0.205 -0.1150 0.690
0.6460 4.4300 0.288 0.205 -0.1140 0.689
0.7460 5.5800 0.288 0.267 -0.2350 0.810
0.8460 7.0200 0.288 0.284 -0.2690 0.845
0.9460 8.8400 0.288 0.295 -0.2910 0.866
1.0500 11.1000 0.288 0.295 -0.2900 0.866
1.1500 14.0000 0.288 0.309 -0.3180 0.893
1.2500 17.6000 0.288 0.279 -0.2600 0.835
1.3500 22.2000 0.288 0.311 -0.3210 0.896
1.4500 28.0000 0.288 0.316 -0.3310 0.906
1.5500 35.2000 0.288 0.317 -0.3340 0.910
1.6500 44.3000 0.313 0.333 -0.3390 0.966
1.7500 55.8000 0.313 0.372 -0.4160 1.040
1.8500 70.2000 0.313 0.404 -0.4790 1.110
1.9500 88.4000 0.313 0.462 -0.5930 1.220
2.0500 111.0000 0.313 0.476 -0.6200 1.250
2.1500 140.0000 0.313 0.559 -0.7830 1.410

IgG Spike Delta1

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.14 1370 0.00522 0.00105 0.003170 0.00727
3.24 1730 0.00594 0.00134 0.003320 0.00855
3.34 2180 0.00594 0.00134 0.003320 0.00855
3.44 2740 0.00594 0.00134 0.003320 0.00855
3.54 3450 0.00594 0.00134 0.003320 0.00855
3.64 4350 0.00594 0.00134 0.003320 0.00855
3.74 5470 0.00599 0.00136 0.003330 0.00865
3.84 6890 0.00599 0.00136 0.003330 0.00865
3.94 8670 0.00599 0.00136 0.003330 0.00866
4.04 10900 0.00601 0.00136 0.003350 0.00867
4.14 13700 0.00608 0.00138 0.003370 0.00878
4.24 17300 0.00610 0.00139 0.003380 0.00882
4.34 21800 0.00621 0.00142 0.003420 0.00900
4.44 27400 0.00625 0.00141 0.003490 0.00901
4.54 34500 0.00625 0.00141 0.003500 0.00901
4.64 43500 0.00641 0.00146 0.003550 0.00926
4.74 54700 0.00646 0.00146 0.003590 0.00932
4.84 68900 0.00661 0.00150 0.003670 0.00954
4.94 86700 0.00650 0.00151 0.003550 0.00946
5.04 109000 0.00668 0.00160 0.003540 0.00982
5.14 137000 0.00689 0.00173 0.003510 0.01030
5.24 173000 0.00628 0.00172 0.002900 0.00966
5.34 218000 0.00637 0.00188 0.002700 0.01010
5.44 274000 0.00524 0.00181 0.001700 0.00879
5.54 345000 0.00510 0.00227 0.000662 0.00954
5.64 435000 0.00240 0.00128 -0.000118 0.00491

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.14 1370 0.0000 0.00616 0.00105 0.004110 0.00821
3.24 1730 0.0117 0.00616 0.00134 0.003540 0.00878
3.34 2180 0.0117 0.00616 0.00134 0.003540 0.00878
3.44 2740 0.0117 0.00616 0.00134 0.003540 0.00878
3.54 3450 0.0117 0.00616 0.00134 0.003540 0.00878
3.64 4350 0.0117 0.00616 0.00134 0.003540 0.00878
3.74 5470 0.0175 0.00616 0.00136 0.003500 0.00882
3.84 6890 0.0175 0.00616 0.00136 0.003500 0.00882
3.94 8670 0.0180 0.00616 0.00136 0.003500 0.00882
4.04 10900 0.0244 0.00616 0.00136 0.003500 0.00882
4.14 13700 0.0308 0.00616 0.00138 0.003450 0.00887
4.24 17300 0.0324 0.00616 0.00139 0.003440 0.00888
4.34 21800 0.0462 0.00616 0.00142 0.003370 0.00895
4.44 27400 0.0680 0.00616 0.00141 0.003400 0.00892
4.54 34500 0.0691 0.00616 0.00141 0.003400 0.00892
4.64 43500 0.0915 0.00616 0.00146 0.003310 0.00901
4.74 54700 0.1060 0.00616 0.00146 0.003290 0.00903
4.84 68900 0.1330 0.00616 0.00150 0.003220 0.00910
4.94 86700 0.1630 0.00616 0.00151 0.003200 0.00911
5.04 109000 0.2070 0.00616 0.00160 0.003020 0.00930
5.14 137000 0.2720 0.00616 0.00173 0.002780 0.00954
5.24 173000 0.3160 0.00616 0.00172 0.002780 0.00953
5.34 218000 0.4380 0.00616 0.00188 0.002480 0.00984
5.44 274000 0.5480 0.00524 0.00181 0.001700 0.00879
5.54 345000 0.6750 0.00510 0.00227 0.000662 0.00954
5.64 435000 0.7490 0.00240 0.00128 -0.000118 0.00491

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.14 1370 0.317 0.157 0.00986 0.624
3.24 1730 0.317 0.182 -0.03920 0.673
3.34 2180 0.317 0.182 -0.03920 0.673
3.44 2740 0.317 0.182 -0.03920 0.673
3.54 3450 0.317 0.182 -0.03920 0.673
3.64 4350 0.317 0.182 -0.03920 0.673
3.74 5470 0.317 0.184 -0.04300 0.677
3.84 6890 0.317 0.184 -0.04300 0.677
3.94 8670 0.317 0.184 -0.04340 0.678
4.04 10900 0.317 0.184 -0.04290 0.677
4.14 13700 0.317 0.186 -0.04750 0.682
4.24 17300 0.317 0.187 -0.04880 0.683
4.34 21800 0.317 0.190 -0.05510 0.689
4.44 27400 0.317 0.188 -0.05210 0.686
4.54 34500 0.317 0.188 -0.05220 0.686
4.64 43500 0.317 0.193 -0.06080 0.695
4.74 54700 0.317 0.193 -0.06210 0.696
4.84 68900 0.317 0.197 -0.06880 0.703
4.94 86700 0.317 0.198 -0.07020 0.704
5.04 109000 0.317 0.207 -0.08780 0.722
5.14 137000 0.317 0.218 -0.11100 0.745
5.24 173000 0.317 0.218 -0.11100 0.745
5.34 218000 0.317 0.233 -0.14000 0.774
5.44 274000 0.419 0.220 -0.01190 0.849
5.54 345000 0.434 0.266 -0.08720 0.956
5.64 435000 0.734 0.148 0.44400 1.020

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 0.006290 0.01170
2.5 317 0.00918 0.00192 0.005430 0.01290
2.6 399 0.00918 0.00192 0.005430 0.01290
2.7 503 0.00918 0.00192 0.005430 0.01290
2.8 633 0.00919 0.00192 0.005430 0.01300
2.9 796 0.00919 0.00192 0.005430 0.01300
3.0 1000 0.00919 0.00192 0.005430 0.01300
3.1 1260 0.00896 0.00190 0.005230 0.01270
3.2 1590 0.00899 0.00190 0.005250 0.01270
3.3 2000 0.00831 0.00185 0.004680 0.01190
3.4 2520 0.00835 0.00186 0.004700 0.01200
3.5 3170 0.00808 0.00183 0.004500 0.01170
3.6 3990 0.00763 0.00178 0.004140 0.01110
3.7 5030 0.00653 0.00162 0.003350 0.00971
3.8 6330 0.00626 0.00159 0.003140 0.00937
3.9 7960 0.00527 0.00146 0.002410 0.00813
4.0 10000 0.00573 0.00158 0.002620 0.00883
4.1 12600 0.00433 0.00141 0.001560 0.00709
4.2 15900 0.00410 0.00140 0.001350 0.00684
4.3 20000 0.00373 0.00142 0.000945 0.00652
4.4 25200 0.00251 0.00107 0.000410 0.00462
4.5 31700 0.00282 0.00127 0.000326 0.00532
4.6 39900 0.00246 0.00120 0.000118 0.00481
4.7 50300 0.00220 0.00126 -0.000264 0.00466
4.8 63300 0.00186 0.00130 -0.000691 0.00442

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.00000 0.00916 0.00139 0.006440 0.01190
2.5 317 0.00380 0.00916 0.00192 0.005410 0.01290
2.6 399 0.00380 0.00916 0.00192 0.005410 0.01290
2.7 503 0.00380 0.00916 0.00192 0.005410 0.01290
2.8 633 0.00430 0.00916 0.00192 0.005400 0.01290
2.9 796 0.00430 0.00916 0.00192 0.005400 0.01290
3.0 1000 0.00430 0.00916 0.00192 0.005400 0.01290
3.1 1260 0.00905 0.00897 0.00190 0.005240 0.01270
3.2 1590 0.01100 0.00897 0.00190 0.005240 0.01270
3.3 2000 0.08490 0.00833 0.00185 0.004700 0.01200
3.4 2520 0.09040 0.00833 0.00186 0.004680 0.01200
3.5 3170 0.09320 0.00808 0.00183 0.004500 0.01170
3.6 3990 0.12100 0.00763 0.00178 0.004140 0.01110
3.7 5030 0.14700 0.00653 0.00162 0.003350 0.00971
3.8 6330 0.15100 0.00626 0.00159 0.003140 0.00937
3.9 7960 0.18500 0.00549 0.00146 0.002630 0.00835
4.0 10000 0.26100 0.00549 0.00158 0.002390 0.00860
4.1 12600 0.33400 0.00433 0.00141 0.001560 0.00709
4.2 15900 0.36300 0.00410 0.00140 0.001350 0.00684
4.3 20000 0.43700 0.00373 0.00142 0.000944 0.00652
4.4 25200 0.45000 0.00267 0.00107 0.000565 0.00477
4.5 31700 0.51500 0.00267 0.00127 0.000171 0.00517
4.6 39900 0.55000 0.00246 0.00120 0.000118 0.00481
4.7 50300 0.61100 0.00220 0.00126 -0.000264 0.00466
4.8 63300 0.65400 0.00186 0.00130 -0.000691 0.00442

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3100 0.0489 0.00584 0.00131 0.003280 0.00841
-1.2100 0.0616 0.00590 0.00132 0.003310 0.00849
-1.1100 0.0776 0.00592 0.00133 0.003310 0.00852
-1.0100 0.0976 0.00592 0.00133 0.003310 0.00852
-0.9100 0.1230 0.00592 0.00133 0.003310 0.00852
-0.8100 0.1550 0.00592 0.00133 0.003310 0.00852
-0.7100 0.1950 0.00592 0.00133 0.003310 0.00852
-0.6100 0.2450 0.00603 0.00138 0.003330 0.00874
-0.5100 0.3090 0.00603 0.00138 0.003330 0.00874
-0.4100 0.3890 0.00603 0.00138 0.003330 0.00874
-0.3100 0.4890 0.00606 0.00137 0.003380 0.00875
-0.2100 0.6160 0.00606 0.00137 0.003380 0.00875
-0.1100 0.7760 0.00615 0.00139 0.003430 0.00888
-0.0104 0.9760 0.00622 0.00140 0.003460 0.00897
0.0896 1.2300 0.00601 0.00138 0.003300 0.00872
0.1900 1.5500 0.00579 0.00136 0.003130 0.00846
0.2900 1.9500 0.00600 0.00142 0.003210 0.00878
0.3900 2.4500 0.00610 0.00145 0.003250 0.00895
0.4900 3.0900 0.00628 0.00151 0.003330 0.00924
0.5900 3.8900 0.00642 0.00163 0.003220 0.00962
0.6900 4.8900 0.00727 0.00199 0.003380 0.01120
0.7900 6.1600 0.00729 0.00197 0.003430 0.01120
0.8900 7.7600 0.00783 0.00216 0.003600 0.01210
0.9900 9.7600 0.00794 0.00215 0.003730 0.01220
1.0900 12.3000 0.00873 0.00238 0.004070 0.01340
1.1900 15.5000 0.00787 0.00226 0.003430 0.01230
1.2900 19.5000 0.00813 0.00252 0.003190 0.01310
1.3900 24.5000 0.00693 0.00246 0.002100 0.01180
1.4900 30.9000 0.00743 0.00263 0.002270 0.01260
1.5900 38.9000 0.00657 0.00266 0.001360 0.01180
1.6900 48.9000 0.00596 0.00327 -0.000448 0.01240
1.7900 61.6000 0.00797 0.00487 -0.001580 0.01750
1.8900 77.6000 0.01090 0.00622 -0.001340 0.02310
1.9900 97.6000 0.01540 0.00967 -0.003590 0.03430
2.0900 123.0000 0.01770 0.00974 -0.001400 0.03680
2.1900 155.0000 0.01600 0.00976 -0.003100 0.03520

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.3100 0.0489 0.00000 0.00648 0.00131 3.92e-03 0.00904
-1.2100 0.0616 0.00583 0.00648 0.00132 3.89e-03 0.00907
-1.1100 0.0776 0.00692 0.00648 0.00133 3.87e-03 0.00909
-1.0100 0.0976 0.00692 0.00648 0.00133 3.87e-03 0.00909
-0.9100 0.1230 0.00692 0.00648 0.00133 3.87e-03 0.00909
-0.8100 0.1550 0.00692 0.00648 0.00133 3.87e-03 0.00909
-0.7100 0.1950 0.00692 0.00648 0.00133 3.87e-03 0.00909
-0.6100 0.2450 0.01970 0.00648 0.00138 3.78e-03 0.00918
-0.5100 0.3090 0.01970 0.00648 0.00138 3.78e-03 0.00918
-0.4100 0.3890 0.01970 0.00648 0.00138 3.78e-03 0.00918
-0.3100 0.4890 0.02920 0.00648 0.00137 3.80e-03 0.00916
-0.2100 0.6160 0.03030 0.00648 0.00137 3.80e-03 0.00916
-0.1100 0.7760 0.05590 0.00648 0.00139 3.75e-03 0.00921
-0.0104 0.9760 0.07390 0.00648 0.00140 3.73e-03 0.00923
0.0896 1.2300 0.08690 0.00648 0.00138 3.77e-03 0.00919
0.1900 1.5500 0.09480 0.00648 0.00136 3.81e-03 0.00915
0.2900 1.9500 0.13100 0.00648 0.00142 3.69e-03 0.00927
0.3900 2.4500 0.14900 0.00648 0.00145 3.63e-03 0.00933
0.4900 3.0900 0.17100 0.00648 0.00151 3.52e-03 0.00944
0.5900 3.8900 0.21500 0.00648 0.00163 3.28e-03 0.00968
0.6900 4.8900 0.28900 0.00648 0.00199 2.59e-03 0.01040
0.7900 6.1600 0.29700 0.00648 0.00197 2.61e-03 0.01030
0.8900 7.7600 0.35200 0.00648 0.00216 2.25e-03 0.01070
0.9900 9.7600 0.37800 0.00648 0.00215 2.26e-03 0.01070
1.0900 12.3000 0.39400 0.00648 0.00238 1.82e-03 0.01110
1.1900 15.5000 0.43200 0.00648 0.00226 2.04e-03 0.01090
1.2900 19.5000 0.48200 0.00648 0.00252 1.54e-03 0.01140
1.3900 24.5000 0.58600 0.00648 0.00246 1.65e-03 0.01130
1.4900 30.9000 0.63100 0.00648 0.00263 1.32e-03 0.01160
1.5900 38.9000 0.65800 0.00648 0.00266 1.27e-03 0.01170
1.6900 48.9000 0.71800 0.00648 0.00327 7.01e-05 0.01290
1.7900 61.6000 0.76200 0.00648 0.00487 -3.07e-03 0.01600
1.8900 77.6000 0.79500 0.00648 0.00622 -5.72e-03 0.01870
1.9900 97.6000 0.85000 0.00648 0.00967 -1.25e-02 0.02540
2.0900 123.0000 0.91500 0.00648 0.00974 -1.26e-02 0.02560
2.1900 155.0000 0.91800 0.00648 0.00976 -1.26e-02 0.02560

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3100 0.0489 0.281 0.179 -0.0687 0.631
-1.2100 0.0616 0.281 0.181 -0.0726 0.635
-1.1100 0.0776 0.281 0.182 -0.0745 0.637
-1.0100 0.0976 0.281 0.182 -0.0745 0.637
-0.9100 0.1230 0.281 0.182 -0.0745 0.637
-0.8100 0.1550 0.281 0.182 -0.0745 0.637
-0.7100 0.1950 0.281 0.182 -0.0745 0.637
-0.6100 0.2450 0.281 0.188 -0.0875 0.650
-0.5100 0.3090 0.281 0.188 -0.0875 0.650
-0.4100 0.3890 0.281 0.188 -0.0875 0.650
-0.3100 0.4890 0.281 0.187 -0.0852 0.648
-0.2100 0.6160 0.281 0.187 -0.0852 0.648
-0.1100 0.7760 0.281 0.190 -0.0912 0.654
-0.0104 0.9760 0.281 0.192 -0.0946 0.657
0.0896 1.2300 0.281 0.189 -0.0883 0.651
0.1900 1.5500 0.281 0.186 -0.0827 0.645
0.2900 1.9500 0.281 0.194 -0.0992 0.662
0.3900 2.4500 0.281 0.198 -0.1070 0.670
0.4900 3.0900 0.281 0.206 -0.1220 0.685
0.5900 3.8900 0.281 0.223 -0.1560 0.718
0.6900 4.8900 0.281 0.271 -0.2510 0.813
0.7900 6.1600 0.281 0.269 -0.2470 0.809
0.8900 7.7600 0.281 0.295 -0.2970 0.859
0.9900 9.7600 0.281 0.294 -0.2940 0.857
1.0900 12.3000 0.281 0.324 -0.3550 0.917
1.1900 15.5000 0.281 0.309 -0.3240 0.887
1.2900 19.5000 0.281 0.344 -0.3940 0.956
1.3900 24.5000 0.281 0.336 -0.3780 0.940
1.4900 30.9000 0.281 0.360 -0.4240 0.987
1.5900 38.9000 0.281 0.363 -0.4300 0.993
1.6900 48.9000 0.281 0.447 -0.5940 1.160
1.7900 61.6000 0.281 0.665 -1.0200 1.590
1.8900 77.6000 0.281 0.850 -1.3800 1.950
1.9900 97.6000 0.281 1.320 -2.3100 2.870
2.0900 123.0000 0.281 1.330 -2.3200 2.890
2.1900 155.0000 0.281 1.330 -2.3300 2.890

IgG Spike Delta2

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.2 1580 0.00522 0.00105 3.17e-03 0.00727
3.3 1990 0.00594 0.00134 3.32e-03 0.00855
3.4 2510 0.00594 0.00134 3.32e-03 0.00855
3.5 3150 0.00594 0.00134 3.32e-03 0.00855
3.6 3970 0.00594 0.00134 3.32e-03 0.00855
3.7 5000 0.00594 0.00134 3.32e-03 0.00855
3.8 6290 0.00599 0.00136 3.33e-03 0.00865
3.9 7920 0.00599 0.00136 3.33e-03 0.00866
4.0 9970 0.00599 0.00136 3.33e-03 0.00866
4.1 12600 0.00601 0.00136 3.35e-03 0.00867
4.2 15800 0.00608 0.00138 3.37e-03 0.00878
4.3 19900 0.00609 0.00138 3.39e-03 0.00880
4.4 25100 0.00621 0.00143 3.41e-03 0.00900
4.5 31500 0.00625 0.00141 3.49e-03 0.00901
4.6 39700 0.00631 0.00143 3.51e-03 0.00911
4.7 50000 0.00641 0.00146 3.55e-03 0.00926
4.8 62900 0.00646 0.00146 3.59e-03 0.00933
4.9 79200 0.00665 0.00151 3.68e-03 0.00961
5.0 99700 0.00658 0.00153 3.58e-03 0.00958
5.1 126000 0.00670 0.00162 3.54e-03 0.00987
5.2 158000 0.00684 0.00171 3.48e-03 0.01020
5.3 199000 0.00623 0.00171 2.87e-03 0.00958
5.4 251000 0.00667 0.00199 2.77e-03 0.01060
5.5 315000 0.00483 0.00173 1.44e-03 0.00823
5.6 397000 0.00338 0.00137 6.94e-04 0.00606
5.7 500000 0.00228 0.00121 -8.78e-05 0.00465

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.2 1580 0.0000 0.00617 0.00105 4.12e-03 0.00822
3.3 1990 0.0117 0.00617 0.00134 3.56e-03 0.00879
3.4 2510 0.0117 0.00617 0.00134 3.56e-03 0.00879
3.5 3150 0.0117 0.00617 0.00134 3.56e-03 0.00879
3.6 3970 0.0117 0.00617 0.00134 3.56e-03 0.00879
3.7 5000 0.0117 0.00617 0.00134 3.56e-03 0.00879
3.8 6290 0.0175 0.00617 0.00136 3.51e-03 0.00883
3.9 7920 0.0180 0.00617 0.00136 3.51e-03 0.00884
4.0 9970 0.0180 0.00617 0.00136 3.51e-03 0.00884
4.1 12600 0.0244 0.00617 0.00136 3.51e-03 0.00883
4.2 15800 0.0313 0.00617 0.00138 3.47e-03 0.00888
4.3 19900 0.0371 0.00617 0.00138 3.47e-03 0.00888
4.4 25100 0.0457 0.00617 0.00143 3.38e-03 0.00897
4.5 31500 0.0680 0.00617 0.00141 3.41e-03 0.00893
4.6 39700 0.0749 0.00617 0.00143 3.38e-03 0.00897
4.7 50000 0.0915 0.00617 0.00146 3.32e-03 0.00903
4.8 62900 0.1070 0.00617 0.00146 3.31e-03 0.00904
4.9 79200 0.1350 0.00617 0.00151 3.21e-03 0.00914
5.0 99700 0.1720 0.00617 0.00153 3.17e-03 0.00918
5.1 126000 0.2040 0.00617 0.00162 3.01e-03 0.00934
5.2 158000 0.2640 0.00617 0.00171 2.81e-03 0.00953
5.3 199000 0.3030 0.00617 0.00171 2.82e-03 0.00953
5.4 251000 0.4580 0.00617 0.00199 2.28e-03 0.01010
5.5 315000 0.5610 0.00483 0.00173 1.44e-03 0.00823
5.6 397000 0.6750 0.00338 0.00137 6.94e-04 0.00606
5.7 500000 0.7520 0.00228 0.00121 -8.79e-05 0.00465

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.2 1580 0.315 0.157 0.00792 0.623
3.3 1990 0.315 0.182 -0.04110 0.672
3.4 2510 0.315 0.182 -0.04110 0.672
3.5 3150 0.315 0.182 -0.04110 0.672
3.6 3970 0.315 0.182 -0.04110 0.672
3.7 5000 0.315 0.182 -0.04110 0.672
3.8 6290 0.315 0.184 -0.04490 0.676
3.9 7920 0.315 0.184 -0.04530 0.676
4.0 9970 0.315 0.184 -0.04530 0.676
4.1 12600 0.315 0.184 -0.04480 0.676
4.2 15800 0.315 0.186 -0.04930 0.680
4.3 19900 0.315 0.186 -0.04900 0.680
4.4 25100 0.315 0.190 -0.05720 0.688
4.5 31500 0.315 0.188 -0.05400 0.685
4.6 39700 0.315 0.190 -0.05750 0.688
4.7 50000 0.315 0.193 -0.06270 0.694
4.8 62900 0.315 0.194 -0.06410 0.695
4.9 79200 0.315 0.198 -0.07300 0.704
5.0 99700 0.315 0.200 -0.07670 0.708
5.1 126000 0.315 0.208 -0.09220 0.723
5.2 158000 0.315 0.217 -0.11100 0.742
5.3 199000 0.315 0.217 -0.11000 0.741
5.4 251000 0.315 0.245 -0.16400 0.795
5.5 315000 0.464 0.209 0.05350 0.874
5.6 397000 0.626 0.162 0.30700 0.944
5.7 500000 0.747 0.140 0.47300 1.020

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 0.006290 0.01170
2.5 317 0.00919 0.00192 0.005430 0.01300
2.6 399 0.00919 0.00192 0.005430 0.01300
2.7 503 0.00919 0.00192 0.005430 0.01300
2.8 633 0.00919 0.00192 0.005430 0.01300
2.9 796 0.00919 0.00192 0.005430 0.01300
3.0 1000 0.00919 0.00192 0.005430 0.01300
3.1 1260 0.00923 0.00194 0.005430 0.01300
3.2 1590 0.00898 0.00190 0.005240 0.01270
3.3 2000 0.00810 0.00179 0.004580 0.01160
3.4 2520 0.00834 0.00186 0.004690 0.01200
3.5 3170 0.00806 0.00182 0.004490 0.01160
3.6 3990 0.00783 0.00180 0.004310 0.01130
3.7 5030 0.00713 0.00171 0.003770 0.01050
3.8 6330 0.00625 0.00159 0.003140 0.00936
3.9 7960 0.00616 0.00160 0.003020 0.00931
4.0 10000 0.00555 0.00154 0.002540 0.00856
4.1 12600 0.00492 0.00148 0.002020 0.00782
4.2 15900 0.00439 0.00143 0.001580 0.00720
4.3 20000 0.00366 0.00139 0.000941 0.00637
4.4 25200 0.00312 0.00126 0.000656 0.00559
4.5 31700 0.00272 0.00120 0.000370 0.00506
4.6 39900 0.00282 0.00124 0.000383 0.00526
4.7 50300 0.00208 0.00114 -0.000158 0.00431
4.8 63300 0.00182 0.00123 -0.000587 0.00424

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.00000 0.00917 0.00139 0.006450 0.01190
2.5 317 0.00430 0.00917 0.00192 0.005410 0.01290
2.6 399 0.00430 0.00917 0.00192 0.005410 0.01290
2.7 503 0.00430 0.00917 0.00192 0.005410 0.01290
2.8 633 0.00430 0.00917 0.00192 0.005410 0.01290
2.9 796 0.00430 0.00917 0.00192 0.005410 0.01290
3.0 1000 0.00430 0.00917 0.00192 0.005410 0.01290
3.1 1260 0.00878 0.00917 0.00194 0.005380 0.01300
3.2 1590 0.01050 0.00898 0.00190 0.005240 0.01270
3.3 2000 0.05470 0.00821 0.00179 0.004700 0.01170
3.4 2520 0.08790 0.00821 0.00186 0.004570 0.01190
3.5 3170 0.09240 0.00806 0.00182 0.004490 0.01160
3.6 3990 0.09590 0.00783 0.00180 0.004310 0.01130
3.7 5030 0.14500 0.00713 0.00171 0.003770 0.01050
3.8 6330 0.15000 0.00625 0.00159 0.003140 0.00936
3.9 7960 0.16200 0.00616 0.00160 0.003020 0.00931
4.0 10000 0.24400 0.00555 0.00154 0.002540 0.00856
4.1 12600 0.27900 0.00492 0.00148 0.002020 0.00782
4.2 15900 0.34300 0.00439 0.00143 0.001580 0.00720
4.3 20000 0.42200 0.00366 0.00139 0.000941 0.00637
4.4 25200 0.44200 0.00312 0.00126 0.000656 0.00559
4.5 31700 0.48900 0.00277 0.00120 0.000423 0.00512
4.6 39900 0.54300 0.00277 0.00124 0.000331 0.00521
4.7 50300 0.57900 0.00208 0.00114 -0.000158 0.00431
4.8 63300 0.64200 0.00182 0.00123 -0.000587 0.00424

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2700 0.0535 0.00584 0.00131 0.003280 0.00841
-1.1700 0.0674 0.00590 0.00132 0.003310 0.00849
-1.0700 0.0848 0.00592 0.00133 0.003310 0.00852
-0.9710 0.1070 0.00592 0.00133 0.003310 0.00852
-0.8710 0.1340 0.00592 0.00133 0.003310 0.00852
-0.7710 0.1690 0.00592 0.00133 0.003310 0.00852
-0.6710 0.2130 0.00592 0.00133 0.003310 0.00852
-0.5710 0.2680 0.00603 0.00138 0.003330 0.00874
-0.4710 0.3380 0.00603 0.00138 0.003330 0.00874
-0.3710 0.4250 0.00603 0.00138 0.003330 0.00874
-0.2710 0.5350 0.00606 0.00137 0.003380 0.00875
-0.1710 0.6740 0.00612 0.00139 0.003400 0.00883
-0.0715 0.8480 0.00615 0.00139 0.003430 0.00888
0.0285 1.0700 0.00596 0.00137 0.003270 0.00865
0.1290 1.3400 0.00579 0.00136 0.003130 0.00845
0.2290 1.6900 0.00584 0.00137 0.003140 0.00853
0.3290 2.1300 0.00600 0.00142 0.003210 0.00879
0.4290 2.6800 0.00611 0.00145 0.003260 0.00895
0.5290 3.3800 0.00606 0.00148 0.003140 0.00897
0.6290 4.2500 0.00669 0.00174 0.003280 0.01010
0.7290 5.3500 0.00728 0.00197 0.003420 0.01110
0.8290 6.7400 0.00746 0.00201 0.003530 0.01140
0.9290 8.4800 0.00781 0.00216 0.003580 0.01200
1.0300 10.7000 0.00799 0.00217 0.003750 0.01220
1.1300 13.4000 0.00852 0.00240 0.003810 0.01320
1.2300 16.9000 0.00717 0.00207 0.003110 0.01120
1.3300 21.3000 0.00738 0.00223 0.003000 0.01180
1.4300 26.8000 0.00701 0.00248 0.002150 0.01190
1.5300 33.8000 0.00676 0.00249 0.001880 0.01160
1.6300 42.5000 0.00657 0.00265 0.001380 0.01180
1.7300 53.5000 0.00654 0.00298 0.000701 0.01240
1.8300 67.4000 0.00687 0.00540 -0.003720 0.01750
1.9300 84.8000 0.01170 0.00621 -0.000465 0.02390
2.0300 107.0000 0.01010 0.00587 -0.001400 0.02160
2.1300 134.0000 0.01710 0.00944 -0.001440 0.03560
2.2300 169.0000 0.01770 0.01060 -0.003040 0.03840

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.2700 0.0535 0.00000 0.00641 0.00131 0.003850 0.00897
-1.1700 0.0674 0.00583 0.00641 0.00132 0.003820 0.00900
-1.0700 0.0848 0.00692 0.00641 0.00133 0.003800 0.00901
-0.9710 0.1070 0.00692 0.00641 0.00133 0.003800 0.00901
-0.8710 0.1340 0.00692 0.00641 0.00133 0.003800 0.00901
-0.7710 0.1690 0.00692 0.00641 0.00133 0.003800 0.00901
-0.6710 0.2130 0.00692 0.00641 0.00133 0.003800 0.00901
-0.5710 0.2680 0.01970 0.00641 0.00138 0.003710 0.00911
-0.4710 0.3380 0.01970 0.00641 0.00138 0.003710 0.00911
-0.3710 0.4250 0.01970 0.00641 0.00138 0.003710 0.00911
-0.2710 0.5350 0.02980 0.00641 0.00137 0.003720 0.00909
-0.1710 0.6740 0.04050 0.00641 0.00139 0.003690 0.00912
-0.0715 0.8480 0.05590 0.00641 0.00139 0.003680 0.00914
0.0285 1.0700 0.07420 0.00641 0.00137 0.003720 0.00910
0.1290 1.3400 0.09320 0.00641 0.00136 0.003750 0.00907
0.2290 1.6900 0.10000 0.00641 0.00137 0.003720 0.00910
0.3290 2.1300 0.13200 0.00641 0.00142 0.003620 0.00920
0.4290 2.6800 0.14900 0.00641 0.00145 0.003560 0.00926
0.5290 3.3800 0.18400 0.00641 0.00148 0.003500 0.00932
0.6290 4.2500 0.23300 0.00641 0.00174 0.003010 0.00981
0.7290 5.3500 0.29400 0.00641 0.00197 0.002550 0.01030
0.8290 6.7400 0.32200 0.00641 0.00201 0.002480 0.01030
0.9290 8.4800 0.34900 0.00641 0.00216 0.002180 0.01060
1.0300 10.7000 0.38400 0.00641 0.00217 0.002160 0.01070
1.1300 13.4000 0.40100 0.00641 0.00240 0.001700 0.01110
1.2300 16.9000 0.42700 0.00641 0.00207 0.002350 0.01050
1.3300 21.3000 0.47200 0.00641 0.00223 0.002030 0.01080
1.4300 26.8000 0.59500 0.00641 0.00248 0.001550 0.01130
1.5300 33.8000 0.62300 0.00641 0.00249 0.001530 0.01130
1.6300 42.5000 0.65900 0.00641 0.00265 0.001220 0.01160
1.7300 53.5000 0.70400 0.00641 0.00298 0.000566 0.01230
1.8300 67.4000 0.77200 0.00641 0.00540 -0.004180 0.01700
1.9300 84.8000 0.82100 0.00641 0.00621 -0.005760 0.01860
2.0300 107.0000 0.85200 0.00641 0.00587 -0.005100 0.01790
2.1300 134.0000 0.91400 0.00641 0.00944 -0.012100 0.02490
2.2300 169.0000 0.93800 0.00641 0.01060 -0.014300 0.02710

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2700 0.0535 0.289 0.178 -0.0594 0.638
-1.1700 0.0674 0.289 0.180 -0.0633 0.642
-1.0700 0.0848 0.289 0.181 -0.0652 0.644
-0.9710 0.1070 0.289 0.181 -0.0652 0.644
-0.8710 0.1340 0.289 0.181 -0.0652 0.644
-0.7710 0.1690 0.289 0.181 -0.0652 0.644
-0.6710 0.2130 0.289 0.181 -0.0652 0.644
-0.5710 0.2680 0.289 0.188 -0.0782 0.657
-0.4710 0.3380 0.289 0.188 -0.0782 0.657
-0.3710 0.4250 0.289 0.188 -0.0782 0.657
-0.2710 0.5350 0.289 0.186 -0.0759 0.655
-0.1710 0.6740 0.289 0.189 -0.0802 0.659
-0.0715 0.8480 0.289 0.189 -0.0818 0.660
0.0285 1.0700 0.289 0.187 -0.0765 0.655
0.1290 1.3400 0.289 0.185 -0.0727 0.651
0.2290 1.6900 0.289 0.187 -0.0771 0.656
0.3290 2.1300 0.289 0.194 -0.0903 0.669
0.4290 2.6800 0.289 0.198 -0.0983 0.677
0.5290 3.3800 0.289 0.202 -0.1070 0.685
0.6290 4.2500 0.289 0.236 -0.1740 0.752
0.7290 5.3500 0.289 0.268 -0.2360 0.814
0.8290 6.7400 0.289 0.273 -0.2450 0.824
0.9290 8.4800 0.289 0.293 -0.2850 0.864
1.0300 10.7000 0.289 0.295 -0.2880 0.867
1.1300 13.4000 0.289 0.327 -0.3510 0.930
1.2300 16.9000 0.289 0.281 -0.2620 0.841
1.3300 21.3000 0.289 0.304 -0.3060 0.885
1.4300 26.8000 0.289 0.337 -0.3710 0.950
1.5300 33.8000 0.289 0.338 -0.3740 0.952
1.6300 42.5000 0.289 0.360 -0.4170 0.995
1.7300 53.5000 0.289 0.406 -0.5060 1.080
1.8300 67.4000 0.289 0.735 -1.1500 1.730
1.9300 84.8000 0.289 0.845 -1.3700 1.950
2.0300 107.0000 0.289 0.799 -1.2800 1.850
2.1300 134.0000 0.289 1.280 -2.2300 2.810
2.2300 169.0000 0.289 1.440 -2.5300 3.110

IgG Spike Delta3

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.1 1260 0.00522 0.00105 0.003170 0.00727
3.2 1580 0.00594 0.00134 0.003320 0.00855
3.3 1990 0.00594 0.00134 0.003320 0.00855
3.4 2510 0.00594 0.00134 0.003320 0.00855
3.5 3160 0.00594 0.00134 0.003320 0.00855
3.6 3970 0.00594 0.00134 0.003320 0.00855
3.7 5000 0.00599 0.00136 0.003330 0.00865
3.8 6300 0.00599 0.00136 0.003330 0.00866
3.9 7930 0.00599 0.00136 0.003330 0.00866
4.0 9980 0.00601 0.00136 0.003350 0.00867
4.1 12600 0.00607 0.00138 0.003370 0.00878
4.2 15800 0.00609 0.00138 0.003390 0.00880
4.3 19900 0.00621 0.00143 0.003410 0.00900
4.4 25100 0.00625 0.00141 0.003490 0.00901
4.5 31600 0.00625 0.00141 0.003490 0.00901
4.6 39700 0.00633 0.00143 0.003530 0.00913
4.7 50000 0.00644 0.00146 0.003570 0.00930
4.8 63000 0.00665 0.00151 0.003680 0.00961
4.9 79300 0.00677 0.00154 0.003750 0.00980
5.0 99800 0.00661 0.00158 0.003520 0.00970
5.1 126000 0.00682 0.00171 0.003470 0.01020
5.2 158000 0.00637 0.00179 0.002870 0.00987
5.3 199000 0.00615 0.00178 0.002670 0.00963
5.4 251000 0.00547 0.00191 0.001730 0.00922
5.5 316000 0.00340 0.00138 0.000696 0.00611
5.6 397000 0.00298 0.00145 0.000143 0.00582

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.1 1260 0.0000 0.00616 0.00105 0.004110 0.00821
3.2 1580 0.0117 0.00616 0.00134 0.003540 0.00878
3.3 1990 0.0117 0.00616 0.00134 0.003540 0.00878
3.4 2510 0.0117 0.00616 0.00134 0.003540 0.00878
3.5 3160 0.0117 0.00616 0.00134 0.003540 0.00878
3.6 3970 0.0117 0.00616 0.00134 0.003540 0.00878
3.7 5000 0.0175 0.00616 0.00136 0.003500 0.00882
3.8 6300 0.0180 0.00616 0.00136 0.003490 0.00882
3.9 7930 0.0180 0.00616 0.00136 0.003490 0.00882
4.0 9980 0.0244 0.00616 0.00136 0.003500 0.00882
4.1 12600 0.0302 0.00616 0.00138 0.003450 0.00886
4.2 15800 0.0371 0.00616 0.00138 0.003450 0.00886
4.3 19900 0.0457 0.00616 0.00143 0.003360 0.00895
4.4 25100 0.0674 0.00616 0.00141 0.003400 0.00892
4.5 31600 0.0685 0.00616 0.00141 0.003400 0.00892
4.6 39700 0.0802 0.00616 0.00143 0.003350 0.00896
4.7 50000 0.1000 0.00616 0.00146 0.003290 0.00902
4.8 63000 0.1360 0.00616 0.00151 0.003190 0.00912
4.9 79300 0.1620 0.00616 0.00154 0.003140 0.00918
5.0 99800 0.1960 0.00616 0.00158 0.003070 0.00925
5.1 126000 0.2610 0.00616 0.00171 0.002810 0.00951
5.2 158000 0.3140 0.00616 0.00179 0.002660 0.00966
5.3 199000 0.4220 0.00615 0.00178 0.002670 0.00963
5.4 251000 0.5580 0.00547 0.00191 0.001730 0.00922
5.5 316000 0.6640 0.00340 0.00138 0.000696 0.00611
5.6 397000 0.7540 0.00298 0.00145 0.000143 0.00582

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.1 1260 0.317 0.157 0.00995 0.624
3.2 1580 0.317 0.182 -0.03920 0.673
3.3 1990 0.317 0.182 -0.03920 0.673
3.4 2510 0.317 0.182 -0.03920 0.673
3.5 3160 0.317 0.182 -0.03920 0.673
3.6 3970 0.317 0.182 -0.03920 0.673
3.7 5000 0.317 0.184 -0.04290 0.677
3.8 6300 0.317 0.184 -0.04330 0.678
3.9 7930 0.317 0.184 -0.04330 0.678
4.0 9980 0.317 0.184 -0.04280 0.677
4.1 12600 0.317 0.186 -0.04730 0.682
4.2 15800 0.317 0.186 -0.04710 0.681
4.3 19900 0.317 0.190 -0.05530 0.690
4.4 25100 0.317 0.188 -0.05200 0.686
4.5 31600 0.317 0.188 -0.05210 0.686
4.6 39700 0.317 0.190 -0.05620 0.690
4.7 50000 0.317 0.193 -0.06170 0.696
4.8 63000 0.317 0.198 -0.07120 0.705
4.9 79300 0.317 0.201 -0.07660 0.711
5.0 99800 0.317 0.204 -0.08310 0.717
5.1 126000 0.317 0.217 -0.10800 0.742
5.2 158000 0.317 0.224 -0.12300 0.757
5.3 199000 0.318 0.223 -0.12000 0.756
5.4 251000 0.393 0.232 -0.06110 0.847
5.5 316000 0.623 0.164 0.30200 0.944
5.6 397000 0.669 0.169 0.33900 1.000

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 0.006290 0.01170
2.5 317 0.00919 0.00192 0.005420 0.01290
2.6 399 0.00919 0.00192 0.005420 0.01290
2.7 503 0.00919 0.00192 0.005420 0.01290
2.8 633 0.00919 0.00192 0.005420 0.01290
2.9 796 0.00919 0.00192 0.005420 0.01290
3.0 1000 0.00919 0.00192 0.005420 0.01290
3.1 1260 0.00888 0.00190 0.005160 0.01260
3.2 1590 0.00855 0.00189 0.004850 0.01230
3.3 2000 0.00835 0.00186 0.004700 0.01200
3.4 2520 0.00806 0.00182 0.004490 0.01160
3.5 3170 0.00752 0.00175 0.004090 0.01100
3.6 3990 0.00675 0.00166 0.003500 0.00999
3.7 5030 0.00625 0.00159 0.003140 0.00936
3.8 6330 0.00538 0.00148 0.002480 0.00829
3.9 7960 0.00550 0.00152 0.002520 0.00847
4.0 10000 0.00474 0.00143 0.001940 0.00754
4.1 12600 0.00433 0.00141 0.001560 0.00710
4.2 15900 0.00379 0.00136 0.001130 0.00646
4.3 20000 0.00311 0.00125 0.000656 0.00557
4.4 25200 0.00261 0.00113 0.000395 0.00482
4.5 31700 0.00284 0.00129 0.000307 0.00537
4.6 39900 0.00207 0.00113 -0.000153 0.00429
4.7 50300 0.00224 0.00132 -0.000335 0.00482

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00916 0.00139 6.43e-03 0.01190
2.5 317 0.0038 0.00916 0.00192 5.40e-03 0.01290
2.6 399 0.0038 0.00916 0.00192 5.40e-03 0.01290
2.7 503 0.0038 0.00916 0.00192 5.40e-03 0.01290
2.8 633 0.0038 0.00916 0.00192 5.40e-03 0.01290
2.9 796 0.0038 0.00916 0.00192 5.40e-03 0.01290
3.0 1000 0.0038 0.00916 0.00192 5.40e-03 0.01290
3.1 1260 0.0370 0.00888 0.00190 5.16e-03 0.01260
3.2 1590 0.0703 0.00855 0.00189 4.85e-03 0.01230
3.3 2000 0.0894 0.00835 0.00186 4.70e-03 0.01200
3.4 2520 0.0929 0.00806 0.00182 4.49e-03 0.01160
3.5 3170 0.0959 0.00752 0.00175 4.09e-03 0.01100
3.6 3990 0.1240 0.00675 0.00166 3.50e-03 0.00999
3.7 5030 0.1500 0.00625 0.00159 3.14e-03 0.00936
3.8 6330 0.2100 0.00544 0.00148 2.54e-03 0.00834
3.9 7960 0.2320 0.00544 0.00152 2.46e-03 0.00842
4.0 10000 0.2910 0.00474 0.00143 1.94e-03 0.00754
4.1 12600 0.3360 0.00433 0.00141 1.56e-03 0.00710
4.2 15900 0.3780 0.00379 0.00136 1.13e-03 0.00646
4.3 20000 0.4400 0.00311 0.00125 6.56e-04 0.00557
4.4 25200 0.4620 0.00272 0.00113 5.09e-04 0.00494
4.5 31700 0.5190 0.00272 0.00129 1.92e-04 0.00525
4.6 39900 0.5750 0.00216 0.00113 -6.42e-05 0.00437
4.7 50300 0.6200 0.00216 0.00132 -4.23e-04 0.00473

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2800 0.0526 0.00584 0.00131 0.003280 0.00841
-1.1800 0.0663 0.00590 0.00132 0.003310 0.00849
-1.0800 0.0834 0.00590 0.00132 0.003310 0.00849
-0.9790 0.1050 0.00592 0.00133 0.003310 0.00852
-0.8790 0.1320 0.00592 0.00133 0.003310 0.00852
-0.7790 0.1660 0.00592 0.00133 0.003310 0.00852
-0.6790 0.2100 0.00596 0.00134 0.003320 0.00859
-0.5790 0.2640 0.00603 0.00138 0.003330 0.00874
-0.4790 0.3320 0.00603 0.00138 0.003330 0.00874
-0.3790 0.4180 0.00603 0.00138 0.003330 0.00874
-0.2790 0.5260 0.00606 0.00137 0.003380 0.00875
-0.1790 0.6630 0.00612 0.00139 0.003400 0.00883
-0.0787 0.8340 0.00615 0.00139 0.003430 0.00888
0.0213 1.0500 0.00596 0.00137 0.003270 0.00865
0.1210 1.3200 0.00604 0.00139 0.003310 0.00876
0.2210 1.6600 0.00589 0.00139 0.003170 0.00862
0.3210 2.1000 0.00600 0.00142 0.003210 0.00879
0.4210 2.6400 0.00611 0.00145 0.003260 0.00896
0.5210 3.3200 0.00636 0.00153 0.003360 0.00936
0.6210 4.1800 0.00648 0.00165 0.003250 0.00971
0.7210 5.2600 0.00728 0.00199 0.003380 0.01120
0.8210 6.6300 0.00761 0.00214 0.003420 0.01180
0.9210 8.3400 0.00780 0.00215 0.003590 0.01200
1.0200 10.5000 0.00795 0.00216 0.003720 0.01220
1.1200 13.2000 0.00833 0.00231 0.003800 0.01290
1.2200 16.6000 0.00754 0.00226 0.003110 0.01200
1.3200 21.0000 0.00768 0.00246 0.002860 0.01250
1.4200 26.4000 0.00703 0.00255 0.002040 0.01200
1.5200 33.2000 0.00597 0.00233 0.001400 0.01050
1.6200 41.8000 0.00581 0.00249 0.000936 0.01070
1.7200 52.6000 0.00548 0.00255 0.000486 0.01050
1.8200 66.3000 0.00929 0.00532 -0.001130 0.01970
1.9200 83.4000 0.01270 0.00665 -0.000338 0.02570
2.0200 105.0000 0.00972 0.00531 -0.000684 0.02010
2.1200 132.0000 0.01760 0.00983 -0.001670 0.03690
2.2200 166.0000 0.01780 0.01060 -0.002910 0.03850

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.2800 0.0526 0.00000 0.00643 0.00131 0.00387 0.00900
-1.1800 0.0663 0.00583 0.00643 0.00132 0.00384 0.00903
-1.0800 0.0834 0.00583 0.00643 0.00132 0.00384 0.00903
-0.9790 0.1050 0.00692 0.00643 0.00133 0.00383 0.00904
-0.8790 0.1320 0.00692 0.00643 0.00133 0.00383 0.00904
-0.7790 0.1660 0.00692 0.00643 0.00133 0.00383 0.00904
-0.6790 0.2100 0.01280 0.00643 0.00134 0.00380 0.00907
-0.5790 0.2640 0.01970 0.00643 0.00138 0.00373 0.00914
-0.4790 0.3320 0.01970 0.00643 0.00138 0.00373 0.00914
-0.3790 0.4180 0.01970 0.00643 0.00138 0.00373 0.00914
-0.2790 0.5260 0.02920 0.00643 0.00137 0.00375 0.00912
-0.1790 0.6630 0.04050 0.00643 0.00139 0.00372 0.00915
-0.0787 0.8340 0.05590 0.00643 0.00139 0.00371 0.00916
0.0213 1.0500 0.07420 0.00643 0.00137 0.00375 0.00912
0.1210 1.3200 0.09240 0.00643 0.00139 0.00371 0.00916
0.2210 1.6600 0.11300 0.00643 0.00139 0.00371 0.00916
0.3210 2.1000 0.13200 0.00643 0.00142 0.00365 0.00922
0.4210 2.6400 0.14900 0.00643 0.00145 0.00358 0.00928
0.5210 3.3200 0.18500 0.00643 0.00153 0.00343 0.00944
0.6210 4.1800 0.23100 0.00643 0.00165 0.00321 0.00966
0.7210 5.2600 0.29000 0.00643 0.00199 0.00254 0.01030
0.8210 6.6300 0.31700 0.00643 0.00214 0.00224 0.01060
0.9210 8.3400 0.34900 0.00643 0.00215 0.00222 0.01060
1.0200 10.5000 0.37700 0.00643 0.00216 0.00220 0.01070
1.1200 13.2000 0.39400 0.00643 0.00231 0.00191 0.01100
1.2200 16.6000 0.44300 0.00643 0.00226 0.00200 0.01090
1.3200 21.0000 0.49900 0.00643 0.00246 0.00161 0.01130
1.4200 26.4000 0.59000 0.00643 0.00255 0.00144 0.01140
1.5200 33.2000 0.60800 0.00643 0.00233 0.00186 0.01100
1.6200 41.8000 0.65800 0.00643 0.00249 0.00156 0.01130
1.7200 52.6000 0.70100 0.00643 0.00255 0.00144 0.01140
1.8200 66.3000 0.77200 0.00643 0.00532 -0.00398 0.01690
1.9200 83.4000 0.81900 0.00643 0.00665 -0.00660 0.01950
2.0200 105.0000 0.86600 0.00643 0.00531 -0.00397 0.01680
2.1200 132.0000 0.91300 0.00643 0.00983 -0.01280 0.02570
2.2200 166.0000 0.92400 0.00643 0.01060 -0.01430 0.02710

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2800 0.0526 0.286 0.178 -0.0627 0.636
-1.1800 0.0663 0.286 0.180 -0.0666 0.640
-1.0800 0.0834 0.286 0.180 -0.0666 0.640
-0.9790 0.1050 0.286 0.181 -0.0685 0.641
-0.8790 0.1320 0.286 0.181 -0.0685 0.641
-0.7790 0.1660 0.286 0.181 -0.0685 0.641
-0.6790 0.2100 0.286 0.183 -0.0721 0.645
-0.5790 0.2640 0.286 0.188 -0.0815 0.654
-0.4790 0.3320 0.286 0.188 -0.0815 0.654
-0.3790 0.4180 0.286 0.188 -0.0815 0.654
-0.2790 0.5260 0.286 0.187 -0.0793 0.652
-0.1790 0.6630 0.286 0.189 -0.0835 0.656
-0.0787 0.8340 0.286 0.190 -0.0852 0.658
0.0213 1.0500 0.286 0.187 -0.0798 0.653
0.1210 1.3200 0.286 0.189 -0.0848 0.658
0.2210 1.6600 0.286 0.189 -0.0848 0.658
0.3210 2.1000 0.286 0.194 -0.0933 0.666
0.4210 2.6400 0.286 0.198 -0.1020 0.675
0.5210 3.3200 0.286 0.209 -0.1220 0.695
0.6210 4.1800 0.286 0.224 -0.1530 0.726
0.7210 5.2600 0.286 0.271 -0.2450 0.817
0.8210 6.6300 0.286 0.292 -0.2850 0.858
0.9210 8.3400 0.286 0.293 -0.2880 0.861
1.0200 10.5000 0.286 0.294 -0.2900 0.863
1.1200 13.2000 0.286 0.315 -0.3310 0.903
1.2200 16.6000 0.286 0.308 -0.3170 0.890
1.3200 21.0000 0.286 0.335 -0.3700 0.943
1.4200 26.4000 0.286 0.347 -0.3940 0.967
1.5200 33.2000 0.286 0.318 -0.3360 0.909
1.6200 41.8000 0.286 0.339 -0.3780 0.951
1.7200 52.6000 0.286 0.347 -0.3950 0.967
1.8200 66.3000 0.286 0.724 -1.1300 1.710
1.9200 83.4000 0.286 0.906 -1.4900 2.060
2.0200 105.0000 0.286 0.723 -1.1300 1.700
2.1200 132.0000 0.286 1.340 -2.3400 2.910
2.2200 166.0000 0.286 1.440 -2.5300 3.110

IgG Spike Omicron

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00522 0.00105 3.17e-03 0.00727
2.5 317 0.00594 0.00134 3.32e-03 0.00855
2.6 399 0.00594 0.00134 3.32e-03 0.00855
2.7 503 0.00594 0.00134 3.32e-03 0.00855
2.8 633 0.00594 0.00134 3.32e-03 0.00855
2.9 796 0.00594 0.00134 3.32e-03 0.00855
3.0 1000 0.00594 0.00134 3.32e-03 0.00855
3.1 1260 0.00594 0.00134 3.32e-03 0.00855
3.2 1590 0.00599 0.00136 3.33e-03 0.00865
3.3 2000 0.00599 0.00136 3.33e-03 0.00866
3.4 2520 0.00600 0.00136 3.34e-03 0.00867
3.5 3170 0.00608 0.00138 3.37e-03 0.00878
3.6 3990 0.00614 0.00141 3.38e-03 0.00890
3.7 5030 0.00626 0.00145 3.42e-03 0.00911
3.8 6330 0.00630 0.00145 3.46e-03 0.00914
3.9 7960 0.00631 0.00143 3.51e-03 0.00911
4.0 10000 0.00633 0.00143 3.53e-03 0.00914
4.1 12600 0.00642 0.00145 3.58e-03 0.00926
4.2 15900 0.00626 0.00144 3.44e-03 0.00908
4.3 20000 0.00659 0.00153 3.60e-03 0.00958
4.4 25200 0.00681 0.00159 3.69e-03 0.00993
4.5 31700 0.00702 0.00165 3.78e-03 0.01030
4.6 39900 0.00719 0.00171 3.85e-03 0.01050
4.7 50300 0.00686 0.00170 3.52e-03 0.01020
4.8 63300 0.00726 0.00206 3.22e-03 0.01130
4.9 79600 0.00723 0.00221 2.90e-03 0.01160
5.0 100000 0.00674 0.00230 2.23e-03 0.01120
5.1 126000 0.00565 0.00287 2.06e-05 0.01130
5.2 159000 0.00238 0.00146 -4.89e-04 0.00524
5.3 200000 0.00371 0.00236 -9.22e-04 0.00834

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00628 0.00105 4.23e-03 0.00833
2.5 317 0.0117 0.00628 0.00134 3.66e-03 0.00890
2.6 399 0.0117 0.00628 0.00134 3.66e-03 0.00890
2.7 503 0.0117 0.00628 0.00134 3.66e-03 0.00890
2.8 633 0.0117 0.00628 0.00134 3.66e-03 0.00890
2.9 796 0.0117 0.00628 0.00134 3.66e-03 0.00890
3.0 1000 0.0117 0.00628 0.00134 3.66e-03 0.00890
3.1 1260 0.0117 0.00628 0.00134 3.66e-03 0.00890
3.2 1590 0.0180 0.00628 0.00136 3.62e-03 0.00894
3.3 2000 0.0186 0.00628 0.00136 3.62e-03 0.00894
3.4 2520 0.0196 0.00628 0.00136 3.61e-03 0.00895
3.5 3170 0.0313 0.00628 0.00138 3.57e-03 0.00899
3.6 3990 0.0377 0.00628 0.00141 3.52e-03 0.00904
3.7 5030 0.0515 0.00628 0.00145 3.43e-03 0.00913
3.8 6330 0.0643 0.00628 0.00145 3.44e-03 0.00912
3.9 7960 0.0738 0.00628 0.00143 3.48e-03 0.00908
4.0 10000 0.0802 0.00628 0.00143 3.47e-03 0.00909
4.1 12600 0.1050 0.00628 0.00145 3.44e-03 0.00912
4.2 15900 0.1250 0.00628 0.00144 3.46e-03 0.00910
4.3 20000 0.1560 0.00628 0.00153 3.29e-03 0.00927
4.4 25200 0.1810 0.00628 0.00159 3.16e-03 0.00940
4.5 31700 0.2120 0.00628 0.00165 3.04e-03 0.00951
4.6 39900 0.2330 0.00628 0.00171 2.94e-03 0.00962
4.7 50300 0.2690 0.00628 0.00170 2.94e-03 0.00962
4.8 63300 0.4170 0.00628 0.00206 2.24e-03 0.01030
4.9 79600 0.5180 0.00628 0.00221 1.95e-03 0.01060
5.0 100000 0.6330 0.00628 0.00230 1.77e-03 0.01080
5.1 126000 0.7360 0.00565 0.00287 2.05e-05 0.01130
5.2 159000 0.7830 0.00304 0.00146 1.78e-04 0.00591
5.3 200000 0.8750 0.00304 0.00236 -1.59e-03 0.00768

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.304 0.158 -0.00633 0.614
2.5 317 0.304 0.183 -0.05510 0.662
2.6 399 0.304 0.183 -0.05510 0.662
2.7 503 0.304 0.183 -0.05510 0.662
2.8 633 0.304 0.183 -0.05510 0.662
2.9 796 0.304 0.183 -0.05510 0.662
3.0 1000 0.304 0.183 -0.05510 0.662
3.1 1260 0.304 0.183 -0.05510 0.662
3.2 1590 0.304 0.185 -0.05860 0.666
3.3 2000 0.304 0.185 -0.05900 0.666
3.4 2520 0.304 0.185 -0.05950 0.667
3.5 3170 0.304 0.187 -0.06310 0.670
3.6 3990 0.304 0.190 -0.06780 0.675
3.7 5030 0.304 0.194 -0.07590 0.683
3.8 6330 0.304 0.193 -0.07530 0.683
3.9 7960 0.304 0.192 -0.07170 0.679
4.0 10000 0.304 0.192 -0.07220 0.679
4.1 12600 0.304 0.193 -0.07530 0.683
4.2 15900 0.304 0.192 -0.07340 0.681
4.3 20000 0.304 0.200 -0.08930 0.697
4.4 25200 0.304 0.207 -0.10200 0.709
4.5 31700 0.304 0.212 -0.11200 0.720
4.6 39900 0.304 0.218 -0.12300 0.730
4.7 50300 0.304 0.217 -0.12200 0.729
4.8 63300 0.304 0.253 -0.19200 0.799
4.9 79600 0.304 0.268 -0.22100 0.828
5.0 100000 0.304 0.277 -0.23900 0.846
5.1 126000 0.373 0.333 -0.28000 1.030
5.2 159000 0.662 0.170 0.32800 0.996
5.3 200000 0.662 0.267 0.13800 1.190

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.001390 0.006290 0.01170
2.5 317 0.00852 0.001870 0.004850 0.01220
2.6 399 0.00852 0.001870 0.004850 0.01220
2.7 503 0.00852 0.001870 0.004850 0.01220
2.8 633 0.00852 0.001870 0.004850 0.01220
2.9 796 0.00822 0.001850 0.004590 0.01180
3.0 1000 0.00834 0.001920 0.004570 0.01210
3.1 1260 0.00802 0.001880 0.004340 0.01170
3.2 1590 0.00747 0.001800 0.003930 0.01100
3.3 2000 0.00700 0.001750 0.003570 0.01040
3.4 2520 0.00624 0.001700 0.002900 0.00958
3.5 3170 0.00573 0.001680 0.002450 0.00901
3.6 3990 0.00356 0.001300 0.001010 0.00612
3.7 5030 0.00335 0.001310 0.000788 0.00591
3.8 6330 0.00250 0.001110 0.000321 0.00468
3.9 7960 0.00174 0.000965 -0.000153 0.00363
4.0 10000 0.00188 0.001090 -0.000257 0.00402
4.1 12600 0.00196 0.001200 -0.000403 0.00432
4.2 15900 0.00216 0.001280 -0.000345 0.00465
4.3 20000 0.00215 0.001440 -0.000664 0.00496

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.0000 0.00902 0.001390 6.29e-03 0.01170
2.5 317 0.0648 0.00852 0.001870 4.85e-03 0.01220
2.6 399 0.0648 0.00852 0.001870 4.85e-03 0.01220
2.7 503 0.0648 0.00852 0.001870 4.85e-03 0.01220
2.8 633 0.0648 0.00852 0.001870 4.85e-03 0.01220
2.9 796 0.1150 0.00828 0.001850 4.65e-03 0.01190
3.0 1000 0.1530 0.00828 0.001920 4.51e-03 0.01200
3.1 1260 0.1550 0.00802 0.001880 4.34e-03 0.01170
3.2 1590 0.1610 0.00747 0.001800 3.93e-03 0.01100
3.3 2000 0.1970 0.00700 0.001750 3.57e-03 0.01040
3.4 2520 0.2490 0.00624 0.001700 2.90e-03 0.00958
3.5 3170 0.2730 0.00573 0.001680 2.45e-03 0.00901
3.6 3990 0.3160 0.00356 0.001300 1.01e-03 0.00612
3.7 5030 0.3780 0.00335 0.001310 7.88e-04 0.00591
3.8 6330 0.3870 0.00250 0.001110 3.21e-04 0.00468
3.9 7960 0.4380 0.00198 0.000965 8.49e-05 0.00387
4.0 10000 0.4970 0.00198 0.001090 -1.64e-04 0.00412
4.1 12600 0.5260 0.00198 0.001200 -3.83e-04 0.00434
4.2 15900 0.6340 0.00198 0.001280 -5.23e-04 0.00448
4.3 20000 0.7060 0.00198 0.001440 -8.36e-04 0.00479

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3200 0.0476 0.00584 0.00131 0.003280 0.00841
-1.2200 0.0599 0.00590 0.00132 0.003310 0.00849
-1.1200 0.0754 0.00592 0.00133 0.003310 0.00852
-1.0200 0.0950 0.00592 0.00133 0.003310 0.00852
-0.9220 0.1200 0.00592 0.00133 0.003310 0.00852
-0.8220 0.1510 0.00592 0.00133 0.003310 0.00852
-0.7220 0.1890 0.00598 0.00135 0.003320 0.00863
-0.6220 0.2390 0.00603 0.00138 0.003330 0.00874
-0.5220 0.3000 0.00603 0.00138 0.003330 0.00874
-0.4220 0.3780 0.00606 0.00137 0.003380 0.00875
-0.3220 0.4760 0.00606 0.00137 0.003380 0.00875
-0.2220 0.5990 0.00612 0.00139 0.003400 0.00883
-0.1220 0.7540 0.00614 0.00139 0.003420 0.00886
-0.0224 0.9500 0.00616 0.00139 0.003430 0.00888
0.0776 1.2000 0.00600 0.00138 0.003280 0.00871
0.1780 1.5100 0.00575 0.00135 0.003100 0.00839
0.2780 1.8900 0.00597 0.00142 0.003180 0.00877
0.3780 2.3900 0.00600 0.00142 0.003200 0.00879
0.4780 3.0000 0.00578 0.00140 0.003030 0.00854
0.5780 3.7800 0.00603 0.00149 0.003120 0.00894
0.6780 4.7600 0.00612 0.00150 0.003170 0.00906
0.7780 5.9900 0.00589 0.00156 0.002840 0.00894
0.8780 7.5400 0.00666 0.00177 0.003200 0.01010
0.9780 9.5000 0.00692 0.00188 0.003230 0.01060
1.0800 12.0000 0.00682 0.00194 0.003030 0.01060
1.1800 15.1000 0.00710 0.00207 0.003060 0.01120
1.2800 18.9000 0.00731 0.00218 0.003040 0.01160
1.3800 23.9000 0.00768 0.00229 0.003190 0.01220
1.4800 30.0000 0.00775 0.00240 0.003040 0.01250
1.5800 37.8000 0.00687 0.00238 0.002210 0.01150
1.6800 47.6000 0.00681 0.00249 0.001940 0.01170
1.7800 59.9000 0.00550 0.00227 0.001060 0.00995
1.8800 75.4000 0.00599 0.00265 0.000796 0.01120
1.9800 95.0000 0.00743 0.00414 -0.000677 0.01550
2.0800 120.0000 0.00981 0.00632 -0.002570 0.02220
2.1800 151.0000 0.00817 0.00651 -0.004590 0.02090
2.2800 189.0000 0.00948 0.00641 -0.003090 0.02200
2.3800 239.0000 0.01280 0.01350 -0.013700 0.03930
2.4800 300.0000 0.01110 0.01690 -0.021900 0.04420

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.3200 0.0476 0.00000 0.00626 0.00131 0.00370 0.00882
-1.2200 0.0599 0.00583 0.00626 0.00132 0.00367 0.00885
-1.1200 0.0754 0.00692 0.00626 0.00133 0.00365 0.00887
-1.0200 0.0950 0.00692 0.00626 0.00133 0.00365 0.00887
-0.9220 0.1200 0.00692 0.00626 0.00133 0.00365 0.00887
-0.8220 0.1510 0.00692 0.00626 0.00133 0.00365 0.00887
-0.7220 0.1890 0.01280 0.00626 0.00135 0.00360 0.00892
-0.6220 0.2390 0.01970 0.00626 0.00138 0.00356 0.00896
-0.5220 0.3000 0.01970 0.00626 0.00138 0.00356 0.00896
-0.4220 0.3780 0.02920 0.00626 0.00137 0.00358 0.00894
-0.3220 0.4760 0.02920 0.00626 0.00137 0.00358 0.00894
-0.2220 0.5990 0.04000 0.00626 0.00139 0.00354 0.00898
-0.1220 0.7540 0.05120 0.00626 0.00139 0.00354 0.00898
-0.0224 0.9500 0.05700 0.00626 0.00139 0.00353 0.00899
0.0776 1.2000 0.08080 0.00626 0.00138 0.00355 0.00897
0.1780 1.5100 0.08160 0.00626 0.00135 0.00361 0.00891
0.2780 1.8900 0.11800 0.00626 0.00142 0.00347 0.00905
0.3780 2.3900 0.12500 0.00626 0.00142 0.00347 0.00905
0.4780 3.0000 0.13800 0.00626 0.00140 0.00351 0.00901
0.5780 3.7800 0.16900 0.00626 0.00149 0.00335 0.00917
0.6780 4.7600 0.19300 0.00626 0.00150 0.00332 0.00920
0.7780 5.9900 0.23800 0.00626 0.00156 0.00321 0.00931
0.8780 7.5400 0.28400 0.00626 0.00177 0.00280 0.00972
0.9780 9.5000 0.30300 0.00626 0.00188 0.00257 0.00995
1.0800 12.0000 0.32200 0.00626 0.00194 0.00246 0.01010
1.1800 15.1000 0.34900 0.00626 0.00207 0.00221 0.01030
1.2800 18.9000 0.36500 0.00626 0.00218 0.00198 0.01050
1.3800 23.9000 0.40900 0.00626 0.00229 0.00177 0.01070
1.4800 30.0000 0.47600 0.00626 0.00240 0.00155 0.01100
1.5800 37.8000 0.56500 0.00626 0.00238 0.00160 0.01090
1.6800 47.6000 0.60600 0.00626 0.00249 0.00139 0.01110
1.7800 59.9000 0.64400 0.00626 0.00227 0.00182 0.01070
1.8800 75.4000 0.71000 0.00626 0.00265 0.00107 0.01150
1.9800 95.0000 0.77000 0.00626 0.00414 -0.00185 0.01440
2.0800 120.0000 0.81400 0.00626 0.00632 -0.00612 0.01860
2.1800 151.0000 0.83000 0.00626 0.00651 -0.00650 0.01900
2.2800 189.0000 0.85800 0.00626 0.00641 -0.00631 0.01880
2.3800 239.0000 0.90300 0.00626 0.01350 -0.02020 0.03280
2.4800 300.0000 0.92100 0.00626 0.01690 -0.02680 0.03930

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3200 0.0476 0.306 0.177 -0.0403 0.652
-1.2200 0.0599 0.306 0.179 -0.0441 0.656
-1.1200 0.0754 0.306 0.179 -0.0460 0.657
-1.0200 0.0950 0.306 0.179 -0.0460 0.657
-0.9220 0.1200 0.306 0.179 -0.0460 0.657
-0.8220 0.1510 0.306 0.179 -0.0460 0.657
-0.7220 0.1890 0.306 0.183 -0.0528 0.664
-0.6220 0.2390 0.306 0.186 -0.0589 0.670
-0.5220 0.3000 0.306 0.186 -0.0589 0.670
-0.4220 0.3780 0.306 0.185 -0.0567 0.668
-0.3220 0.4760 0.306 0.185 -0.0567 0.668
-0.2220 0.5990 0.306 0.187 -0.0609 0.672
-0.1220 0.7540 0.306 0.188 -0.0619 0.673
-0.0224 0.9500 0.306 0.188 -0.0625 0.674
0.0776 1.2000 0.306 0.187 -0.0603 0.672
0.1780 1.5100 0.306 0.182 -0.0520 0.663
0.2780 1.8900 0.306 0.192 -0.0713 0.683
0.3780 2.3900 0.306 0.192 -0.0711 0.683
0.4780 3.0000 0.306 0.190 -0.0660 0.677
0.5780 3.7800 0.306 0.201 -0.0877 0.699
0.6780 4.7600 0.306 0.203 -0.0917 0.703
0.7780 5.9900 0.306 0.210 -0.1060 0.717
0.8780 7.5400 0.306 0.238 -0.1620 0.773
0.9780 9.5000 0.306 0.254 -0.1920 0.804
1.0800 12.0000 0.306 0.261 -0.2070 0.818
1.1800 15.1000 0.306 0.279 -0.2410 0.852
1.2800 18.9000 0.306 0.295 -0.2720 0.883
1.3800 23.9000 0.306 0.309 -0.3000 0.911
1.4800 30.0000 0.306 0.325 -0.3310 0.942
1.5800 37.8000 0.306 0.321 -0.3240 0.935
1.6800 47.6000 0.306 0.336 -0.3520 0.964
1.7800 59.9000 0.306 0.306 -0.2940 0.906
1.8800 75.4000 0.306 0.358 -0.3950 1.010
1.9800 95.0000 0.306 0.559 -0.7890 1.400
2.0800 120.0000 0.306 0.853 -1.3700 1.980
2.1800 151.0000 0.306 0.879 -1.4200 2.030
2.2800 189.0000 0.306 0.866 -1.3900 2.000
2.3800 239.0000 0.306 1.830 -3.2700 3.880
2.4800 300.0000 0.306 2.280 -4.1500 4.760

IgG Spike Cross-Reactivity Score

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.06 1150 0.00522 0.00105 0.003170 0.00727
3.16 1450 0.00594 0.00134 0.003320 0.00855
3.26 1830 0.00594 0.00134 0.003320 0.00855
3.36 2300 0.00594 0.00134 0.003320 0.00855
3.46 2900 0.00594 0.00134 0.003320 0.00855
3.56 3650 0.00599 0.00136 0.003330 0.00865
3.66 4590 0.00599 0.00136 0.003330 0.00865
3.76 5780 0.00599 0.00136 0.003330 0.00866
3.86 7280 0.00600 0.00136 0.003330 0.00866
3.96 9160 0.00608 0.00138 0.003370 0.00878
4.06 11500 0.00608 0.00138 0.003370 0.00878
4.16 14500 0.00613 0.00139 0.003400 0.00887
4.26 18300 0.00626 0.00145 0.003420 0.00910
4.36 23000 0.00631 0.00143 0.003510 0.00910
4.46 29000 0.00634 0.00143 0.003530 0.00914
4.56 36500 0.00634 0.00143 0.003530 0.00914
4.66 45900 0.00648 0.00146 0.003610 0.00934
4.76 57800 0.00676 0.00154 0.003740 0.00977
4.86 72800 0.00686 0.00161 0.003710 0.01000
4.96 91600 0.00704 0.00166 0.003790 0.01030
5.06 115000 0.00685 0.00172 0.003480 0.01020
5.16 145000 0.00663 0.00176 0.003180 0.01010
5.26 183000 0.00604 0.00198 0.002170 0.00992
5.36 230000 0.00572 0.00198 0.001830 0.00960
5.46 290000 0.00550 0.00243 0.000743 0.01020
5.56 365000 0.00262 0.00142 -0.000159 0.00539

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
3.06 1150 0.0000 0.00621 0.00105 0.004160 0.00826
3.16 1450 0.0117 0.00621 0.00134 0.003600 0.00883
3.26 1830 0.0117 0.00621 0.00134 0.003600 0.00883
3.36 2300 0.0117 0.00621 0.00134 0.003600 0.00883
3.46 2900 0.0117 0.00621 0.00134 0.003600 0.00883
3.56 3650 0.0175 0.00621 0.00136 0.003550 0.00887
3.66 4590 0.0175 0.00621 0.00136 0.003550 0.00887
3.76 5780 0.0180 0.00621 0.00136 0.003550 0.00888
3.86 7280 0.0186 0.00621 0.00136 0.003550 0.00888
3.96 9160 0.0313 0.00621 0.00138 0.003510 0.00892
4.06 11500 0.0313 0.00621 0.00138 0.003510 0.00892
4.16 14500 0.0393 0.00621 0.00139 0.003480 0.00895
4.26 18300 0.0521 0.00621 0.00145 0.003370 0.00905
4.36 23000 0.0733 0.00621 0.00143 0.003420 0.00901
4.46 29000 0.0813 0.00621 0.00143 0.003410 0.00902
4.56 36500 0.0813 0.00621 0.00143 0.003410 0.00902
4.66 45900 0.1150 0.00621 0.00146 0.003350 0.00908
4.76 57800 0.1590 0.00621 0.00154 0.003200 0.00923
4.86 72800 0.1840 0.00621 0.00161 0.003060 0.00937
4.96 91600 0.2150 0.00621 0.00166 0.002970 0.00946
5.06 115000 0.2570 0.00621 0.00172 0.002840 0.00959
5.16 145000 0.3240 0.00621 0.00176 0.002760 0.00967
5.26 183000 0.4690 0.00604 0.00198 0.002170 0.00992
5.36 230000 0.6100 0.00572 0.00198 0.001830 0.00960
5.46 290000 0.7100 0.00550 0.00243 0.000743 0.01020
5.56 365000 0.7920 0.00262 0.00142 -0.000159 0.00539

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
3.06 1150 0.311 0.157 0.00252 0.619
3.16 1450 0.311 0.182 -0.04640 0.668
3.26 1830 0.311 0.182 -0.04640 0.668
3.36 2300 0.311 0.182 -0.04640 0.668
3.46 2900 0.311 0.182 -0.04640 0.668
3.56 3650 0.311 0.184 -0.05010 0.672
3.66 4590 0.311 0.184 -0.05010 0.672
3.76 5780 0.311 0.184 -0.05050 0.672
3.86 7280 0.311 0.185 -0.05090 0.673
3.96 9160 0.311 0.186 -0.05450 0.676
4.06 11500 0.311 0.186 -0.05450 0.676
4.16 14500 0.311 0.188 -0.05690 0.679
4.26 18300 0.311 0.193 -0.06690 0.689
4.36 23000 0.311 0.191 -0.06270 0.685
4.46 29000 0.311 0.191 -0.06370 0.686
4.56 36500 0.311 0.191 -0.06370 0.686
4.66 45900 0.311 0.194 -0.06900 0.691
4.76 57800 0.311 0.201 -0.08300 0.705
4.86 72800 0.311 0.208 -0.09630 0.718
4.96 91600 0.311 0.212 -0.10500 0.727
5.06 115000 0.311 0.218 -0.11700 0.739
5.16 145000 0.311 0.223 -0.12500 0.747
5.26 183000 0.330 0.242 -0.14500 0.805
5.36 230000 0.366 0.240 -0.10500 0.837
5.46 290000 0.391 0.285 -0.16800 0.949
5.56 365000 0.710 0.163 0.39000 1.030

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
2.4 252 0.00902 0.00139 6.29e-03 0.01170
2.5 317 0.00917 0.00191 5.42e-03 0.01290
2.6 399 0.00917 0.00191 5.42e-03 0.01290
2.7 503 0.00919 0.00192 5.43e-03 0.01300
2.8 633 0.00927 0.00193 5.48e-03 0.01300
2.9 796 0.00932 0.00194 5.51e-03 0.01310
3.0 1000 0.00932 0.00194 5.51e-03 0.01310
3.1 1260 0.00853 0.00184 4.92e-03 0.01210
3.2 1590 0.00848 0.00186 4.83e-03 0.01210
3.3 2000 0.00865 0.00190 4.92e-03 0.01240
3.4 2520 0.00821 0.00186 4.57e-03 0.01190
3.5 3170 0.00741 0.00175 3.98e-03 0.01080
3.6 3990 0.00741 0.00179 3.91e-03 0.01090
3.7 5030 0.00665 0.00169 3.34e-03 0.00997
3.8 6330 0.00586 0.00159 2.74e-03 0.00898
3.9 7960 0.00540 0.00157 2.33e-03 0.00847
4.0 10000 0.00429 0.00146 1.42e-03 0.00716
4.1 12600 0.00305 0.00122 6.53e-04 0.00545
4.2 15900 0.00314 0.00127 6.55e-04 0.00562
4.3 20000 0.00258 0.00111 3.99e-04 0.00476
4.4 25200 0.00233 0.00111 1.51e-04 0.00452
4.5 31700 0.00251 0.00125 7.08e-05 0.00496
4.6 39900 0.00206 0.00116 -2.25e-04 0.00434
4.7 50300 0.00173 0.00120 -6.19e-04 0.00408

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
2.4 252 0.00000 0.00921 0.00139 6.48e-03 0.01190
2.5 317 0.00279 0.00921 0.00191 5.46e-03 0.01300
2.6 399 0.00279 0.00921 0.00191 5.46e-03 0.01300
2.7 503 0.00430 0.00921 0.00192 5.45e-03 0.01300
2.8 633 0.01760 0.00921 0.00193 5.43e-03 0.01300
2.9 796 0.02160 0.00921 0.00194 5.40e-03 0.01300
3.0 1000 0.02210 0.00921 0.00194 5.40e-03 0.01300
3.1 1260 0.02850 0.00855 0.00184 4.95e-03 0.01220
3.2 1590 0.06190 0.00855 0.00186 4.90e-03 0.01220
3.3 2000 0.09140 0.00855 0.00190 4.82e-03 0.01230
3.4 2520 0.11700 0.00821 0.00186 4.57e-03 0.01190
3.5 3170 0.14500 0.00741 0.00175 3.98e-03 0.01080
3.6 3990 0.16300 0.00741 0.00179 3.91e-03 0.01090
3.7 5030 0.20800 0.00665 0.00169 3.34e-03 0.00997
3.8 6330 0.21900 0.00586 0.00159 2.74e-03 0.00898
3.9 7960 0.25500 0.00540 0.00157 2.33e-03 0.00847
4.0 10000 0.30600 0.00429 0.00146 1.42e-03 0.00716
4.1 12600 0.43100 0.00309 0.00122 6.96e-04 0.00549
4.2 15900 0.44500 0.00309 0.00127 6.11e-04 0.00558
4.3 20000 0.47600 0.00258 0.00111 3.99e-04 0.00476
4.4 25200 0.52300 0.00242 0.00111 2.41e-04 0.00461
4.5 31700 0.57000 0.00242 0.00125 -1.99e-05 0.00487
4.6 39900 0.61700 0.00206 0.00116 -2.25e-04 0.00434
4.7 50300 0.66400 0.00173 0.00120 -6.19e-04 0.00408

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1400 0.0727 0.00584 0.00131 3.28e-03 0.00841
-1.0400 0.0915 0.00592 0.00133 3.31e-03 0.00852
-0.9380 0.1150 0.00592 0.00133 3.31e-03 0.00852
-0.8380 0.1450 0.00592 0.00133 3.31e-03 0.00852
-0.7380 0.1830 0.00592 0.00133 3.31e-03 0.00852
-0.6380 0.2300 0.00599 0.00136 3.32e-03 0.00866
-0.5380 0.2890 0.00603 0.00138 3.33e-03 0.00874
-0.4380 0.3640 0.00603 0.00138 3.33e-03 0.00874
-0.3380 0.4590 0.00606 0.00137 3.38e-03 0.00875
-0.2380 0.5780 0.00606 0.00137 3.38e-03 0.00875
-0.1380 0.7270 0.00613 0.00139 3.42e-03 0.00885
-0.0384 0.9150 0.00618 0.00140 3.44e-03 0.00891
0.0616 1.1500 0.00599 0.00138 3.28e-03 0.00870
0.1620 1.4500 0.00579 0.00136 3.13e-03 0.00845
0.2620 1.8300 0.00582 0.00137 3.14e-03 0.00850
0.3620 2.3000 0.00600 0.00142 3.21e-03 0.00879
0.4620 2.8900 0.00607 0.00145 3.23e-03 0.00890
0.5620 3.6400 0.00617 0.00152 3.20e-03 0.00915
0.6620 4.5900 0.00606 0.00155 3.03e-03 0.00909
0.7620 5.7800 0.00728 0.00197 3.42e-03 0.01110
0.8620 7.2700 0.00740 0.00198 3.51e-03 0.01130
0.9620 9.1500 0.00771 0.00211 3.58e-03 0.01180
1.0600 11.5000 0.00785 0.00218 3.57e-03 0.01210
1.1600 14.5000 0.00845 0.00240 3.75e-03 0.01320
1.2600 18.3000 0.00783 0.00239 3.14e-03 0.01250
1.3600 23.0000 0.00738 0.00223 3.02e-03 0.01180
1.4600 28.9000 0.00632 0.00229 1.82e-03 0.01080
1.5600 36.4000 0.00596 0.00232 1.42e-03 0.01050
1.6600 45.9000 0.00565 0.00241 9.31e-04 0.01040
1.7600 57.8000 0.00680 0.00330 3.27e-04 0.01330
1.8600 72.7000 0.00508 0.00320 -1.20e-03 0.01140
1.9600 91.5000 0.00660 0.00331 9.96e-05 0.01310

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.1400 0.0727 0.00000 0.00640 0.00131 0.003840 0.00896
-1.0400 0.0915 0.00692 0.00640 0.00133 0.003790 0.00900
-0.9380 0.1150 0.00692 0.00640 0.00133 0.003790 0.00900
-0.8380 0.1450 0.00692 0.00640 0.00133 0.003790 0.00900
-0.7380 0.1830 0.00692 0.00640 0.00133 0.003790 0.00900
-0.6380 0.2300 0.01380 0.00640 0.00136 0.003730 0.00907
-0.5380 0.2890 0.01970 0.00640 0.00138 0.003700 0.00910
-0.4380 0.3640 0.01970 0.00640 0.00138 0.003700 0.00910
-0.3380 0.4590 0.02920 0.00640 0.00137 0.003710 0.00908
-0.2380 0.5780 0.02920 0.00640 0.00137 0.003710 0.00908
-0.1380 0.7270 0.04690 0.00640 0.00139 0.003680 0.00911
-0.0384 0.9150 0.06230 0.00640 0.00140 0.003660 0.00914
0.0616 1.1500 0.08050 0.00640 0.00138 0.003690 0.00911
0.1620 1.4500 0.09320 0.00640 0.00136 0.003740 0.00906
0.2620 1.8300 0.10100 0.00640 0.00137 0.003720 0.00908
0.3620 2.3000 0.13200 0.00640 0.00142 0.003610 0.00919
0.4620 2.8900 0.14000 0.00640 0.00145 0.003560 0.00923
0.5620 3.6400 0.20100 0.00640 0.00152 0.003420 0.00937
0.6620 4.5900 0.22000 0.00640 0.00155 0.003370 0.00943
0.7620 5.7800 0.29600 0.00640 0.00197 0.002540 0.01030
0.8620 7.2700 0.31300 0.00640 0.00198 0.002520 0.01030
0.9620 9.1500 0.34100 0.00640 0.00211 0.002270 0.01050
1.0600 11.5000 0.34800 0.00640 0.00218 0.002120 0.01070
1.1600 14.5000 0.38500 0.00640 0.00240 0.001690 0.01110
1.2600 18.3000 0.42600 0.00640 0.00239 0.001700 0.01110
1.3600 23.0000 0.47100 0.00640 0.00223 0.002030 0.01080
1.4600 28.9000 0.56700 0.00632 0.00229 0.001820 0.01080
1.5600 36.4000 0.61600 0.00614 0.00232 0.001600 0.01070
1.6600 45.9000 0.64500 0.00614 0.00241 0.001420 0.01090
1.7600 57.8000 0.69100 0.00614 0.00330 -0.000334 0.01260
1.8600 72.7000 0.75100 0.00584 0.00320 -0.000442 0.01210
1.9600 91.5000 0.80000 0.00584 0.00331 -0.000658 0.01230

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.1400 0.0727 0.290 0.178 -0.0581 0.639
-1.0400 0.0915 0.290 0.181 -0.0639 0.645
-0.9380 0.1150 0.290 0.181 -0.0639 0.645
-0.8380 0.1450 0.290 0.181 -0.0639 0.645
-0.7380 0.1830 0.290 0.181 -0.0639 0.645
-0.6380 0.2300 0.290 0.185 -0.0728 0.654
-0.5380 0.2890 0.290 0.187 -0.0769 0.658
-0.4380 0.3640 0.290 0.187 -0.0769 0.658
-0.3380 0.4590 0.290 0.186 -0.0746 0.655
-0.2380 0.5780 0.290 0.186 -0.0746 0.655
-0.1380 0.7270 0.290 0.188 -0.0789 0.660
-0.0384 0.9150 0.290 0.190 -0.0818 0.663
0.0616 1.1500 0.290 0.188 -0.0777 0.659
0.1620 1.4500 0.290 0.185 -0.0714 0.652
0.2620 1.8300 0.290 0.186 -0.0738 0.655
0.3620 2.3000 0.290 0.194 -0.0889 0.670
0.4620 2.8900 0.290 0.197 -0.0952 0.676
0.5620 3.6400 0.290 0.206 -0.1140 0.695
0.6620 4.5900 0.290 0.210 -0.1220 0.702
0.7620 5.7800 0.290 0.268 -0.2340 0.815
0.8620 7.2700 0.290 0.269 -0.2380 0.818
0.9620 9.1500 0.290 0.287 -0.2710 0.852
1.0600 11.5000 0.290 0.297 -0.2920 0.873
1.1600 14.5000 0.290 0.326 -0.3490 0.930
1.2600 18.3000 0.290 0.326 -0.3480 0.929
1.3600 23.0000 0.290 0.303 -0.3030 0.884
1.4600 28.9000 0.300 0.310 -0.3080 0.908
1.5600 36.4000 0.320 0.311 -0.2890 0.929
1.6600 45.9000 0.320 0.323 -0.3130 0.952
1.7600 57.8000 0.320 0.443 -0.5480 1.190
1.8600 72.7000 0.352 0.423 -0.4770 1.180
1.9600 91.5000 0.352 0.438 -0.5060 1.210

nAb ID50 Reference

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 0.003170 0.00727
1.4 25.2 0.00596 0.00132 0.003370 0.00854
1.5 31.7 0.00596 0.00132 0.003370 0.00854
1.6 39.9 0.00596 0.00132 0.003370 0.00854
1.7 50.2 0.00596 0.00132 0.003370 0.00854
1.8 63.2 0.00596 0.00132 0.003370 0.00854
1.9 79.6 0.00596 0.00132 0.003370 0.00854
2.0 100.0 0.00596 0.00132 0.003370 0.00855
2.1 126.0 0.00602 0.00133 0.003410 0.00863
2.2 159.0 0.00610 0.00136 0.003430 0.00877
2.3 200.0 0.00609 0.00134 0.003460 0.00872
2.4 252.0 0.00609 0.00134 0.003470 0.00871
2.5 317.0 0.00610 0.00134 0.003480 0.00871
2.6 399.0 0.00584 0.00130 0.003290 0.00840
2.7 502.0 0.00562 0.00128 0.003110 0.00814
2.8 632.0 0.00572 0.00131 0.003150 0.00829
2.9 796.0 0.00577 0.00133 0.003170 0.00838
3.0 1000.0 0.00557 0.00131 0.003010 0.00813
3.1 1260.0 0.00561 0.00132 0.003020 0.00819
3.2 1590.0 0.00570 0.00135 0.003050 0.00834
3.3 2000.0 0.00575 0.00136 0.003080 0.00842
3.4 2520.0 0.00590 0.00141 0.003140 0.00866
3.5 3170.0 0.00570 0.00138 0.003010 0.00840
3.6 3990.0 0.00574 0.00142 0.002950 0.00853
3.7 5020.0 0.00606 0.00153 0.003080 0.00905
3.8 6320.0 0.00607 0.00157 0.002990 0.00914
3.9 7960.0 0.00460 0.00137 0.001910 0.00730
4.0 10000.0 0.00402 0.00138 0.001310 0.00673
4.1 12600.0 0.00359 0.00134 0.000961 0.00622
4.2 15900.0 0.00357 0.00142 0.000793 0.00634
4.3 20000.0 0.00376 0.00183 0.000171 0.00735

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00595 0.00105 3.90e-03 0.00800
1.4 25.2 0.0122 0.00595 0.00132 3.36e-03 0.00853
1.5 31.7 0.0122 0.00595 0.00132 3.36e-03 0.00853
1.6 39.9 0.0122 0.00595 0.00132 3.36e-03 0.00853
1.7 50.2 0.0122 0.00595 0.00132 3.36e-03 0.00853
1.8 63.2 0.0122 0.00595 0.00132 3.36e-03 0.00853
1.9 79.6 0.0122 0.00595 0.00132 3.36e-03 0.00853
2.0 100.0 0.0127 0.00595 0.00132 3.36e-03 0.00853
2.1 126.0 0.0221 0.00595 0.00133 3.34e-03 0.00855
2.2 159.0 0.0297 0.00595 0.00136 3.28e-03 0.00862
2.3 200.0 0.0336 0.00595 0.00134 3.31e-03 0.00858
2.4 252.0 0.0366 0.00595 0.00134 3.33e-03 0.00857
2.5 317.0 0.0396 0.00595 0.00134 3.33e-03 0.00856
2.6 399.0 0.0398 0.00584 0.00130 3.29e-03 0.00840
2.7 502.0 0.0431 0.00576 0.00128 3.25e-03 0.00828
2.8 632.0 0.0534 0.00576 0.00131 3.19e-03 0.00833
2.9 796.0 0.0634 0.00576 0.00133 3.15e-03 0.00837
3.0 1000.0 0.0750 0.00576 0.00131 3.20e-03 0.00832
3.1 1260.0 0.0784 0.00576 0.00132 3.17e-03 0.00835
3.2 1590.0 0.0921 0.00576 0.00135 3.12e-03 0.00841
3.3 2000.0 0.1010 0.00576 0.00136 3.09e-03 0.00843
3.4 2520.0 0.1240 0.00576 0.00141 3.00e-03 0.00852
3.5 3170.0 0.1590 0.00576 0.00138 3.07e-03 0.00846
3.6 3990.0 0.1880 0.00576 0.00142 2.97e-03 0.00855
3.7 5020.0 0.2290 0.00576 0.00153 2.77e-03 0.00875
3.8 6320.0 0.2670 0.00576 0.00157 2.68e-03 0.00884
3.9 7960.0 0.3050 0.00460 0.00137 1.91e-03 0.00730
4.0 10000.0 0.3750 0.00402 0.00138 1.31e-03 0.00673
4.1 12600.0 0.4860 0.00364 0.00134 1.01e-03 0.00627
4.2 15900.0 0.5560 0.00364 0.00142 8.64e-04 0.00641
4.3 20000.0 0.6910 0.00364 0.00183 5.05e-05 0.00723

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.341 0.139 0.06830 0.613
1.4 25.2 0.341 0.175 -0.00241 0.684
1.5 31.7 0.341 0.175 -0.00241 0.684
1.6 39.9 0.341 0.175 -0.00241 0.684
1.7 50.2 0.341 0.175 -0.00241 0.684
1.8 63.2 0.341 0.175 -0.00241 0.684
1.9 79.6 0.341 0.175 -0.00241 0.684
2.0 100.0 0.341 0.175 -0.00284 0.684
2.1 126.0 0.341 0.177 -0.00586 0.687
2.2 159.0 0.341 0.181 -0.01400 0.695
2.3 200.0 0.341 0.178 -0.00899 0.690
2.4 252.0 0.341 0.178 -0.00731 0.689
2.5 317.0 0.341 0.177 -0.00711 0.688
2.6 399.0 0.352 0.172 0.01450 0.690
2.7 502.0 0.361 0.169 0.03020 0.692
2.8 632.0 0.361 0.173 0.02240 0.700
2.9 796.0 0.361 0.175 0.01820 0.704
3.0 1000.0 0.361 0.172 0.02400 0.698
3.1 1260.0 0.361 0.174 0.02070 0.702
3.2 1590.0 0.361 0.178 0.01310 0.709
3.3 2000.0 0.361 0.179 0.00943 0.713
3.4 2520.0 0.361 0.185 -0.00228 0.725
3.5 3170.0 0.361 0.181 0.00637 0.716
3.6 3990.0 0.361 0.187 -0.00590 0.728
3.7 5020.0 0.361 0.201 -0.03230 0.755
3.8 6320.0 0.361 0.207 -0.04410 0.766
3.9 7960.0 0.490 0.171 0.15400 0.825
4.0 10000.0 0.554 0.168 0.22600 0.883
4.1 12600.0 0.597 0.160 0.28200 0.911
4.2 15900.0 0.597 0.169 0.26500 0.928
4.3 20000.0 0.597 0.219 0.16800 1.030

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.00139 0.006290 0.01170
1.4 25.2 0.00781 0.00176 0.004360 0.01130
1.5 31.7 0.00781 0.00176 0.004360 0.01130
1.6 39.9 0.00781 0.00176 0.004360 0.01130
1.7 50.2 0.00783 0.00176 0.004380 0.01130
1.8 63.2 0.00783 0.00176 0.004380 0.01130
1.9 79.6 0.00758 0.00173 0.004180 0.01100
2.0 100.0 0.00733 0.00171 0.003980 0.01070
2.1 126.0 0.00748 0.00174 0.004070 0.01090
2.2 159.0 0.00660 0.00163 0.003400 0.00980
2.3 200.0 0.00561 0.00150 0.002680 0.00854
2.4 252.0 0.00536 0.00152 0.002390 0.00833
2.5 317.0 0.00511 0.00150 0.002180 0.00804
2.6 399.0 0.00444 0.00140 0.001700 0.00719
2.7 502.0 0.00450 0.00142 0.001710 0.00728
2.8 632.0 0.00418 0.00139 0.001460 0.00691
2.9 796.0 0.00271 0.00116 0.000435 0.00498
3.0 1000.0 0.00218 0.00105 0.000110 0.00424
3.1 1260.0 0.00223 0.00108 0.000117 0.00435
3.2 1590.0 0.00245 0.00116 0.000164 0.00473
3.3 2000.0 0.00256 0.00122 0.000174 0.00494
3.4 2520.0 0.00211 0.00115 -0.000153 0.00437

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.00139 6.29e-03 0.01170
1.4 25.2 0.210 0.00782 0.00176 4.37e-03 0.01130
1.5 31.7 0.210 0.00782 0.00176 4.37e-03 0.01130
1.6 39.9 0.210 0.00782 0.00176 4.37e-03 0.01130
1.7 50.2 0.211 0.00782 0.00176 4.36e-03 0.01130
1.8 63.2 0.212 0.00782 0.00176 4.36e-03 0.01130
1.9 79.6 0.214 0.00758 0.00173 4.18e-03 0.01100
2.0 100.0 0.226 0.00741 0.00171 4.06e-03 0.01080
2.1 126.0 0.235 0.00741 0.00174 4.00e-03 0.01080
2.2 159.0 0.243 0.00660 0.00163 3.40e-03 0.00980
2.3 200.0 0.258 0.00561 0.00150 2.68e-03 0.00854
2.4 252.0 0.282 0.00536 0.00152 2.39e-03 0.00833
2.5 317.0 0.298 0.00511 0.00150 2.18e-03 0.00804
2.6 399.0 0.316 0.00447 0.00140 1.72e-03 0.00721
2.7 502.0 0.323 0.00447 0.00142 1.68e-03 0.00725
2.8 632.0 0.347 0.00418 0.00139 1.46e-03 0.00691
2.9 796.0 0.388 0.00271 0.00116 4.35e-04 0.00498
3.0 1000.0 0.438 0.00235 0.00105 2.87e-04 0.00442
3.1 1260.0 0.461 0.00235 0.00108 2.36e-04 0.00447
3.2 1590.0 0.528 0.00235 0.00116 7.28e-05 0.00463
3.3 2000.0 0.560 0.00235 0.00122 -3.14e-05 0.00474
3.4 2520.0 0.605 0.00211 0.00115 -1.53e-04 0.00437

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.4400 0.0360 0.00522 0.00105 3.17e-03 0.00727
-1.3400 0.0454 0.00578 0.00126 3.32e-03 0.00825
-1.2400 0.0571 0.00578 0.00126 3.32e-03 0.00825
-1.1400 0.0719 0.00578 0.00126 3.32e-03 0.00825
-1.0400 0.0905 0.00578 0.00126 3.32e-03 0.00825
-0.9430 0.1140 0.00578 0.00126 3.32e-03 0.00825
-0.8430 0.1430 0.00579 0.00126 3.33e-03 0.00825
-0.7430 0.1810 0.00581 0.00126 3.34e-03 0.00829
-0.6430 0.2270 0.00587 0.00128 3.36e-03 0.00837
-0.5430 0.2860 0.00587 0.00128 3.37e-03 0.00837
-0.4430 0.3600 0.00592 0.00129 3.39e-03 0.00844
-0.3430 0.4540 0.00596 0.00130 3.41e-03 0.00850
-0.2430 0.5710 0.00598 0.00130 3.43e-03 0.00853
-0.1430 0.7190 0.00606 0.00132 3.47e-03 0.00866
-0.0433 0.9050 0.00621 0.00136 3.55e-03 0.00887
0.0567 1.1400 0.00618 0.00139 3.46e-03 0.00890
0.1570 1.4300 0.00632 0.00143 3.53e-03 0.00912
0.2570 1.8100 0.00608 0.00140 3.34e-03 0.00883
0.3570 2.2700 0.00613 0.00142 3.35e-03 0.00890
0.4570 2.8600 0.00587 0.00144 3.05e-03 0.00868
0.5570 3.6000 0.00598 0.00147 3.10e-03 0.00886
0.6570 4.5400 0.00612 0.00151 3.16e-03 0.00908
0.7570 5.7100 0.00626 0.00154 3.25e-03 0.00927
0.8570 7.1900 0.00655 0.00162 3.37e-03 0.00974
0.9570 9.0500 0.00652 0.00164 3.31e-03 0.00973
1.0600 11.4000 0.00738 0.00191 3.64e-03 0.01110
1.1600 14.3000 0.00730 0.00191 3.56e-03 0.01100
1.2600 18.1000 0.00763 0.00201 3.70e-03 0.01160
1.3600 22.7000 0.00601 0.00186 2.37e-03 0.00964
1.4600 28.6000 0.00572 0.00179 2.22e-03 0.00923
1.5600 36.0000 0.00691 0.00208 2.83e-03 0.01100
1.6600 45.4000 0.00620 0.00205 2.18e-03 0.01020
1.7600 57.1000 0.00674 0.00226 2.30e-03 0.01120
1.8600 71.9000 0.00717 0.00258 2.11e-03 0.01220
1.9600 90.5000 0.00669 0.00255 1.70e-03 0.01170
2.0600 114.0000 0.00685 0.00302 9.35e-04 0.01280
2.1600 143.0000 0.00458 0.00237 -6.69e-05 0.00922
2.2600 181.0000 0.00510 0.00267 -1.46e-04 0.01030
2.3600 227.0000 0.00471 0.00285 -8.73e-04 0.01030

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.4400 0.0360 0.00000 0.00614 0.00105 0.004090 0.00819
-1.3400 0.0454 0.00300 0.00614 0.00126 0.003680 0.00860
-1.2400 0.0571 0.00300 0.00614 0.00126 0.003680 0.00860
-1.1400 0.0719 0.00300 0.00614 0.00126 0.003680 0.00860
-1.0400 0.0905 0.00300 0.00614 0.00126 0.003680 0.00860
-0.9430 0.1140 0.00300 0.00614 0.00126 0.003680 0.00860
-0.8430 0.1430 0.00601 0.00614 0.00126 0.003680 0.00860
-0.7430 0.1810 0.01010 0.00614 0.00126 0.003670 0.00861
-0.6430 0.2270 0.01420 0.00614 0.00128 0.003640 0.00864
-0.5430 0.2860 0.01470 0.00614 0.00128 0.003640 0.00864
-0.4430 0.3600 0.02790 0.00614 0.00129 0.003620 0.00866
-0.3430 0.4540 0.03480 0.00614 0.00130 0.003600 0.00868
-0.2430 0.5710 0.04160 0.00614 0.00130 0.003590 0.00869
-0.1430 0.7190 0.05530 0.00614 0.00132 0.003550 0.00873
-0.0433 0.9050 0.08310 0.00614 0.00136 0.003480 0.00880
0.0567 1.1400 0.09730 0.00614 0.00139 0.003420 0.00886
0.1570 1.4300 0.11200 0.00614 0.00143 0.003340 0.00894
0.2570 1.8100 0.11700 0.00614 0.00140 0.003390 0.00889
0.3570 2.2700 0.12100 0.00614 0.00142 0.003360 0.00892
0.4570 2.8600 0.16100 0.00614 0.00144 0.003330 0.00895
0.5570 3.6000 0.18200 0.00614 0.00147 0.003260 0.00902
0.6570 4.5400 0.20200 0.00614 0.00151 0.003180 0.00910
0.7570 5.7100 0.23700 0.00614 0.00154 0.003130 0.00915
0.8570 7.1900 0.26900 0.00614 0.00162 0.002960 0.00932
0.9570 9.0500 0.29600 0.00614 0.00164 0.002930 0.00935
1.0600 11.4000 0.33000 0.00614 0.00191 0.002400 0.00988
1.1600 14.3000 0.36900 0.00614 0.00191 0.002400 0.00988
1.2600 18.1000 0.39200 0.00614 0.00201 0.002210 0.01010
1.3600 22.7000 0.41500 0.00614 0.00186 0.002500 0.00978
1.4600 28.6000 0.46700 0.00614 0.00179 0.002630 0.00965
1.5600 36.0000 0.52000 0.00614 0.00208 0.002060 0.01020
1.6600 45.4000 0.56200 0.00614 0.00205 0.002120 0.01020
1.7600 57.1000 0.59400 0.00614 0.00226 0.001710 0.01060
1.8600 71.9000 0.64900 0.00614 0.00258 0.001080 0.01120
1.9600 90.5000 0.69000 0.00614 0.00255 0.001150 0.01110
2.0600 114.0000 0.74000 0.00614 0.00302 0.000225 0.01210
2.1600 143.0000 0.77800 0.00484 0.00237 0.000193 0.00948
2.2600 181.0000 0.80300 0.00484 0.00267 -0.000406 0.01010
2.3600 227.0000 0.83000 0.00471 0.00285 -0.000873 0.01030

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.4400 0.0360 0.319 0.140 0.0440 0.594
-1.3400 0.0454 0.319 0.169 -0.0113 0.649
-1.2400 0.0571 0.319 0.169 -0.0113 0.649
-1.1400 0.0719 0.319 0.169 -0.0113 0.649
-1.0400 0.0905 0.319 0.169 -0.0113 0.649
-0.9430 0.1140 0.319 0.169 -0.0113 0.649
-0.8430 0.1430 0.319 0.169 -0.0113 0.649
-0.7430 0.1810 0.319 0.169 -0.0127 0.651
-0.6430 0.2270 0.319 0.171 -0.0164 0.655
-0.5430 0.2860 0.319 0.171 -0.0164 0.655
-0.4430 0.3600 0.319 0.173 -0.0195 0.658
-0.3430 0.4540 0.319 0.174 -0.0222 0.660
-0.2430 0.5710 0.319 0.175 -0.0232 0.661
-0.1430 0.7190 0.319 0.177 -0.0288 0.667
-0.0433 0.9050 0.319 0.182 -0.0380 0.676
0.0567 1.1400 0.319 0.186 -0.0457 0.684
0.1570 1.4300 0.319 0.192 -0.0564 0.695
0.2570 1.8100 0.319 0.188 -0.0494 0.688
0.3570 2.2700 0.319 0.190 -0.0534 0.692
0.4570 2.8600 0.319 0.193 -0.0583 0.696
0.5570 3.6000 0.319 0.197 -0.0669 0.705
0.6570 4.5400 0.319 0.203 -0.0785 0.717
0.7570 5.7100 0.319 0.206 -0.0849 0.723
0.8570 7.1900 0.319 0.218 -0.1080 0.746
0.9570 9.0500 0.319 0.220 -0.1120 0.750
1.0600 11.4000 0.319 0.256 -0.1830 0.821
1.1600 14.3000 0.319 0.256 -0.1830 0.821
1.2600 18.1000 0.319 0.269 -0.2090 0.847
1.3600 22.7000 0.319 0.249 -0.1690 0.807
1.4600 28.6000 0.319 0.240 -0.1510 0.790
1.5600 36.0000 0.319 0.279 -0.2290 0.867
1.6600 45.4000 0.319 0.275 -0.2200 0.858
1.7600 57.1000 0.319 0.304 -0.2760 0.914
1.8600 71.9000 0.319 0.347 -0.3600 0.998
1.9600 90.5000 0.319 0.342 -0.3510 0.989
2.0600 114.0000 0.319 0.405 -0.4750 1.110
2.1600 143.0000 0.464 0.298 -0.1210 1.050
2.2600 181.0000 0.464 0.337 -0.1960 1.120
2.3600 227.0000 0.478 0.356 -0.2210 1.180

nAb ID50 B.1.351

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 3.17e-03 0.00727
1.4 25.2 0.00600 0.00132 3.41e-03 0.00858
1.5 31.7 0.00600 0.00132 3.41e-03 0.00858
1.6 39.9 0.00600 0.00132 3.41e-03 0.00858
1.7 50.2 0.00600 0.00132 3.41e-03 0.00858
1.8 63.2 0.00600 0.00132 3.41e-03 0.00858
1.9 79.6 0.00604 0.00133 3.43e-03 0.00865
2.0 100.0 0.00610 0.00136 3.44e-03 0.00877
2.1 126.0 0.00612 0.00137 3.44e-03 0.00880
2.2 159.0 0.00618 0.00139 3.45e-03 0.00891
2.3 200.0 0.00572 0.00132 3.14e-03 0.00830
2.4 252.0 0.00573 0.00131 3.15e-03 0.00830
2.5 317.0 0.00577 0.00132 3.18e-03 0.00836
2.6 399.0 0.00583 0.00134 3.19e-03 0.00846
2.7 502.0 0.00555 0.00131 2.99e-03 0.00811
2.8 632.0 0.00567 0.00134 3.05e-03 0.00830
2.9 796.0 0.00569 0.00134 3.06e-03 0.00831
3.0 1000.0 0.00562 0.00137 2.94e-03 0.00831
3.1 1260.0 0.00542 0.00135 2.77e-03 0.00807
3.2 1590.0 0.00559 0.00145 2.76e-03 0.00843
3.3 2000.0 0.00570 0.00147 2.82e-03 0.00857
3.4 2520.0 0.00546 0.00144 2.65e-03 0.00827
3.5 3170.0 0.00465 0.00133 2.04e-03 0.00726
3.6 3990.0 0.00479 0.00137 2.10e-03 0.00747
3.7 5020.0 0.00333 0.00116 1.06e-03 0.00560
3.8 6320.0 0.00321 0.00116 9.31e-04 0.00548
3.9 7960.0 0.00322 0.00125 7.69e-04 0.00568
4.0 10000.0 0.00237 0.00124 -5.19e-05 0.00479

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00596 0.00105 3.91e-03 0.00801
1.4 25.2 0.0187 0.00596 0.00132 3.38e-03 0.00855
1.5 31.7 0.0187 0.00596 0.00132 3.38e-03 0.00855
1.6 39.9 0.0187 0.00596 0.00132 3.38e-03 0.00855
1.7 50.2 0.0187 0.00596 0.00132 3.38e-03 0.00855
1.8 63.2 0.0187 0.00596 0.00132 3.38e-03 0.00855
1.9 79.6 0.0222 0.00596 0.00133 3.35e-03 0.00858
2.0 100.0 0.0287 0.00596 0.00136 3.30e-03 0.00863
2.1 126.0 0.0298 0.00596 0.00137 3.28e-03 0.00865
2.2 159.0 0.0361 0.00596 0.00139 3.23e-03 0.00869
2.3 200.0 0.0466 0.00576 0.00132 3.18e-03 0.00834
2.4 252.0 0.0502 0.00576 0.00131 3.19e-03 0.00834
2.5 317.0 0.0600 0.00576 0.00132 3.17e-03 0.00835
2.6 399.0 0.0662 0.00576 0.00134 3.13e-03 0.00840
2.7 502.0 0.0667 0.00564 0.00131 3.08e-03 0.00820
2.8 632.0 0.0960 0.00564 0.00134 3.01e-03 0.00826
2.9 796.0 0.1010 0.00564 0.00134 3.01e-03 0.00827
3.0 1000.0 0.1310 0.00562 0.00137 2.94e-03 0.00831
3.1 1260.0 0.1400 0.00557 0.00135 2.92e-03 0.00821
3.2 1590.0 0.1650 0.00557 0.00145 2.73e-03 0.00840
3.3 2000.0 0.1930 0.00557 0.00147 2.69e-03 0.00844
3.4 2520.0 0.2040 0.00546 0.00144 2.65e-03 0.00827
3.5 3170.0 0.2340 0.00472 0.00133 2.11e-03 0.00733
3.6 3990.0 0.2860 0.00472 0.00137 2.03e-03 0.00740
3.7 5020.0 0.3750 0.00333 0.00116 1.06e-03 0.00560
3.8 6320.0 0.4160 0.00321 0.00116 9.40e-04 0.00549
3.9 7960.0 0.4900 0.00321 0.00125 7.60e-04 0.00567
4.0 10000.0 0.6000 0.00237 0.00124 -5.19e-05 0.00479

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.339 0.139 0.06600 0.611
1.4 25.2 0.339 0.175 -0.00512 0.682
1.5 31.7 0.339 0.175 -0.00512 0.682
1.6 39.9 0.339 0.175 -0.00512 0.682
1.7 50.2 0.339 0.175 -0.00512 0.682
1.8 63.2 0.339 0.175 -0.00512 0.682
1.9 79.6 0.339 0.177 -0.00899 0.686
2.0 100.0 0.339 0.181 -0.01580 0.693
2.1 126.0 0.339 0.182 -0.01800 0.695
2.2 159.0 0.339 0.185 -0.02450 0.702
2.3 200.0 0.361 0.173 0.02160 0.701
2.4 252.0 0.361 0.173 0.02240 0.700
2.5 317.0 0.361 0.174 0.02010 0.702
2.6 399.0 0.361 0.177 0.01450 0.708
2.7 502.0 0.375 0.171 0.03990 0.710
2.8 632.0 0.375 0.175 0.03140 0.718
2.9 796.0 0.375 0.175 0.03110 0.718
3.0 1000.0 0.377 0.179 0.02590 0.728
3.1 1260.0 0.383 0.176 0.03750 0.728
3.2 1590.0 0.383 0.188 0.01330 0.752
3.3 2000.0 0.383 0.191 0.00822 0.757
3.4 2520.0 0.395 0.186 0.02960 0.759
3.5 3170.0 0.477 0.167 0.15000 0.803
3.6 3990.0 0.477 0.171 0.14100 0.813
3.7 5020.0 0.631 0.137 0.36300 0.899
3.8 6320.0 0.644 0.137 0.37600 0.911
3.9 7960.0 0.644 0.147 0.35500 0.932
4.0 10000.0 0.737 0.142 0.46000 1.010

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.00139 0.006290 0.01170
1.4 25.2 0.00614 0.00160 0.003010 0.00927
1.5 31.7 0.00614 0.00160 0.003010 0.00927
1.6 39.9 0.00614 0.00160 0.003010 0.00927
1.7 50.2 0.00614 0.00160 0.003010 0.00927
1.8 63.2 0.00571 0.00152 0.002730 0.00869
1.9 79.6 0.00547 0.00150 0.002530 0.00842
2.0 100.0 0.00545 0.00155 0.002410 0.00848
2.1 126.0 0.00513 0.00151 0.002170 0.00808
2.2 159.0 0.00458 0.00147 0.001700 0.00747
2.3 200.0 0.00421 0.00141 0.001450 0.00698
2.4 252.0 0.00345 0.00128 0.000951 0.00595
2.5 317.0 0.00351 0.00143 0.000711 0.00632

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.00139 0.006290 0.01170
1.4 25.2 0.280 0.00614 0.00160 0.003010 0.00927
1.5 31.7 0.280 0.00614 0.00160 0.003010 0.00927
1.6 39.9 0.280 0.00614 0.00160 0.003010 0.00927
1.7 50.2 0.280 0.00614 0.00160 0.003010 0.00927
1.8 63.2 0.282 0.00571 0.00152 0.002730 0.00869
1.9 79.6 0.297 0.00547 0.00150 0.002530 0.00842
2.0 100.0 0.319 0.00545 0.00155 0.002410 0.00848
2.1 126.0 0.330 0.00513 0.00151 0.002170 0.00808
2.2 159.0 0.360 0.00458 0.00147 0.001700 0.00747
2.3 200.0 0.384 0.00421 0.00141 0.001450 0.00698
2.4 252.0 0.390 0.00348 0.00128 0.000982 0.00598
2.5 317.0 0.422 0.00348 0.00143 0.000679 0.00628

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2500 0.0562 0.00522 0.00105 0.003170 0.00727
-1.1500 0.0707 0.00582 0.00127 0.003340 0.00830
-1.0500 0.0890 0.00582 0.00127 0.003340 0.00830
-0.9500 0.1120 0.00582 0.00127 0.003340 0.00830
-0.8500 0.1410 0.00586 0.00127 0.003360 0.00836
-0.7500 0.1780 0.00589 0.00128 0.003380 0.00840
-0.6500 0.2240 0.00589 0.00128 0.003380 0.00840
-0.5500 0.2820 0.00590 0.00128 0.003380 0.00841
-0.4500 0.3540 0.00596 0.00130 0.003410 0.00851
-0.3500 0.4460 0.00601 0.00132 0.003430 0.00859
-0.2500 0.5620 0.00602 0.00131 0.003440 0.00859
-0.1500 0.7070 0.00604 0.00132 0.003450 0.00862
-0.0504 0.8900 0.00607 0.00133 0.003470 0.00867
0.0496 1.1200 0.00611 0.00137 0.003420 0.00880
0.1500 1.4100 0.00613 0.00138 0.003430 0.00884
0.2500 1.7800 0.00618 0.00139 0.003450 0.00892
0.3500 2.2400 0.00632 0.00143 0.003520 0.00912
0.4500 2.8200 0.00589 0.00139 0.003170 0.00862
0.5500 3.5400 0.00606 0.00144 0.003240 0.00887
0.6500 4.4600 0.00627 0.00151 0.003310 0.00923
0.7500 5.6200 0.00639 0.00153 0.003400 0.00938
0.8500 7.0700 0.00631 0.00154 0.003290 0.00933
0.9500 8.9000 0.00618 0.00155 0.003150 0.00921
1.0500 11.2000 0.00575 0.00153 0.002760 0.00875
1.1500 14.1000 0.00523 0.00148 0.002330 0.00812
1.2500 17.8000 0.00505 0.00146 0.002190 0.00791
1.3500 22.4000 0.00440 0.00137 0.001720 0.00708
1.4500 28.2000 0.00458 0.00143 0.001780 0.00739
1.5500 35.4000 0.00493 0.00156 0.001860 0.00799
1.6500 44.6000 0.00433 0.00151 0.001380 0.00728
1.7500 56.2000 0.00453 0.00160 0.001410 0.00766
1.8500 70.7000 0.00553 0.00198 0.001640 0.00942
1.9500 89.0000 0.00631 0.00220 0.002010 0.01060
2.0500 112.0000 0.00737 0.00258 0.002310 0.01240
2.1500 141.0000 0.00558 0.00239 0.000907 0.01030
2.2500 178.0000 0.00521 0.00240 0.000507 0.00992
2.3500 224.0000 0.00520 0.00271 -0.000110 0.01050

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.2500 0.0562 0.00000 0.00600 0.00105 3.95e-03 0.00805
-1.1500 0.0707 0.00601 0.00600 0.00127 3.52e-03 0.00848
-1.0500 0.0890 0.00601 0.00600 0.00127 3.52e-03 0.00848
-0.9500 0.1120 0.00601 0.00600 0.00127 3.52e-03 0.00848
-0.8500 0.1410 0.01120 0.00600 0.00127 3.50e-03 0.00850
-0.7500 0.1780 0.01810 0.00600 0.00128 3.49e-03 0.00851
-0.6500 0.2240 0.01810 0.00600 0.00128 3.49e-03 0.00851
-0.5500 0.2820 0.02110 0.00600 0.00128 3.49e-03 0.00852
-0.4500 0.3540 0.02540 0.00600 0.00130 3.45e-03 0.00855
-0.3500 0.4460 0.03170 0.00600 0.00132 3.42e-03 0.00858
-0.2500 0.5620 0.03470 0.00600 0.00131 3.43e-03 0.00858
-0.1500 0.7070 0.04140 0.00600 0.00132 3.42e-03 0.00858
-0.0504 0.8900 0.05020 0.00600 0.00133 3.40e-03 0.00860
0.0496 1.1200 0.07930 0.00600 0.00137 3.31e-03 0.00869
0.1500 1.4100 0.08310 0.00600 0.00138 3.30e-03 0.00871
0.2500 1.7800 0.08980 0.00600 0.00139 3.27e-03 0.00873
0.3500 2.2400 0.11400 0.00600 0.00143 3.20e-03 0.00880
0.4500 2.8200 0.13900 0.00600 0.00139 3.28e-03 0.00873
0.5500 3.5400 0.16200 0.00600 0.00144 3.19e-03 0.00882
0.6500 4.4600 0.18600 0.00600 0.00151 3.05e-03 0.00896
0.7500 5.6200 0.21600 0.00600 0.00153 3.01e-03 0.00899
0.8500 7.0700 0.22800 0.00600 0.00154 2.98e-03 0.00902
0.9500 8.9000 0.24500 0.00600 0.00155 2.97e-03 0.00904
1.0500 11.2000 0.27800 0.00575 0.00153 2.76e-03 0.00875
1.1500 14.1000 0.30400 0.00523 0.00148 2.33e-03 0.00812
1.2500 17.8000 0.35500 0.00505 0.00146 2.19e-03 0.00791
1.3500 22.4000 0.36900 0.00463 0.00137 1.95e-03 0.00731
1.4500 28.2000 0.39800 0.00463 0.00143 1.83e-03 0.00744
1.5500 35.4000 0.45000 0.00463 0.00156 1.57e-03 0.00770
1.6500 44.6000 0.46700 0.00463 0.00151 1.68e-03 0.00759
1.7500 56.2000 0.49300 0.00463 0.00160 1.51e-03 0.00776
1.8500 70.7000 0.54800 0.00463 0.00198 7.45e-04 0.00852
1.9500 89.0000 0.60200 0.00463 0.00220 3.28e-04 0.00894
2.0500 112.0000 0.63400 0.00463 0.00258 -4.28e-04 0.00970
2.1500 141.0000 0.66900 0.00463 0.00239 -4.12e-05 0.00931
2.2500 178.0000 0.72800 0.00463 0.00240 -7.25e-05 0.00934
2.3500 224.0000 0.78200 0.00463 0.00271 -6.74e-04 0.00994

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.2500 0.0562 0.335 0.139 6.14e-02 0.608
-1.1500 0.0707 0.335 0.169 3.94e-03 0.665
-1.0500 0.0890 0.335 0.169 3.94e-03 0.665
-0.9500 0.1120 0.335 0.169 3.94e-03 0.665
-0.8500 0.1410 0.335 0.170 1.67e-03 0.667
-0.7500 0.1780 0.335 0.171 -3.64e-05 0.669
-0.6500 0.2240 0.335 0.171 -3.64e-05 0.669
-0.5500 0.2820 0.335 0.171 -4.76e-04 0.669
-0.4500 0.3540 0.335 0.173 -5.10e-03 0.674
-0.3500 0.4460 0.335 0.175 -8.91e-03 0.678
-0.2500 0.5620 0.335 0.175 -8.50e-03 0.678
-0.1500 0.7070 0.335 0.176 -9.56e-03 0.679
-0.0504 0.8900 0.335 0.177 -1.21e-02 0.681
0.0496 1.1200 0.335 0.183 -2.40e-02 0.693
0.1500 1.4100 0.335 0.184 -2.57e-02 0.695
0.2500 1.7800 0.335 0.186 -2.95e-02 0.699
0.3500 2.2400 0.335 0.190 -3.82e-02 0.707
0.4500 2.8200 0.335 0.185 -2.84e-02 0.697
0.5500 3.5400 0.335 0.191 -4.04e-02 0.709
0.6500 4.4600 0.335 0.201 -5.92e-02 0.728
0.7500 5.6200 0.335 0.203 -6.41e-02 0.733
0.8500 7.0700 0.335 0.205 -6.78e-02 0.737
0.9500 8.9000 0.335 0.206 -6.97e-02 0.739
1.0500 11.2000 0.362 0.201 -3.16e-02 0.755
1.1500 14.1000 0.421 0.189 4.92e-02 0.792
1.2500 17.8000 0.440 0.186 7.61e-02 0.804
1.3500 22.4000 0.486 0.170 1.52e-01 0.820
1.4500 28.2000 0.486 0.179 1.36e-01 0.836
1.5500 35.4000 0.486 0.195 1.04e-01 0.868
1.6500 44.6000 0.486 0.188 1.18e-01 0.854
1.7500 56.2000 0.486 0.199 9.62e-02 0.876
1.8500 70.7000 0.486 0.247 1.09e-03 0.971
1.9500 89.0000 0.486 0.274 -5.10e-02 1.020
2.0500 112.0000 0.486 0.322 -1.45e-01 1.120
2.1500 141.0000 0.486 0.297 -9.70e-02 1.070
2.2500 178.0000 0.486 0.299 -1.01e-01 1.070
2.3500 224.0000 0.486 0.338 -1.76e-01 1.150

nAb ID50 BA.1

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 3.17e-03 0.00727
1.4 25.2 0.00594 0.00135 3.29e-03 0.00860
1.5 31.7 0.00594 0.00135 3.29e-03 0.00860
1.6 39.9 0.00594 0.00135 3.29e-03 0.00860
1.7 50.2 0.00594 0.00135 3.29e-03 0.00860
1.8 63.2 0.00596 0.00136 3.29e-03 0.00863
1.9 79.6 0.00596 0.00136 3.30e-03 0.00863
2.0 100.0 0.00572 0.00132 3.12e-03 0.00831
2.1 126.0 0.00579 0.00134 3.15e-03 0.00842
2.2 159.0 0.00587 0.00136 3.21e-03 0.00854
2.3 200.0 0.00614 0.00144 3.31e-03 0.00896
2.4 252.0 0.00618 0.00143 3.37e-03 0.00898
2.5 317.0 0.00633 0.00148 3.43e-03 0.00922
2.6 399.0 0.00648 0.00152 3.50e-03 0.00947
2.7 502.0 0.00665 0.00157 3.57e-03 0.00973
2.8 632.0 0.00653 0.00157 3.44e-03 0.00962
2.9 796.0 0.00711 0.00173 3.72e-03 0.01050
3.0 1000.0 0.00668 0.00170 3.34e-03 0.01000
3.1 1260.0 0.00699 0.00187 3.33e-03 0.01060
3.2 1590.0 0.00643 0.00181 2.89e-03 0.00998
3.3 2000.0 0.00515 0.00172 1.78e-03 0.00853
3.4 2520.0 0.00271 0.00137 2.84e-05 0.00540
3.5 3170.0 0.00202 0.00127 -4.64e-04 0.00451

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00616 0.00105 4.11e-03 0.00820
1.4 25.2 0.0410 0.00616 0.00135 3.50e-03 0.00881
1.5 31.7 0.0410 0.00616 0.00135 3.50e-03 0.00881
1.6 39.9 0.0410 0.00616 0.00135 3.50e-03 0.00881
1.7 50.2 0.0410 0.00616 0.00135 3.50e-03 0.00881
1.8 63.2 0.0421 0.00616 0.00136 3.49e-03 0.00882
1.9 79.6 0.0423 0.00616 0.00136 3.49e-03 0.00882
2.0 100.0 0.0458 0.00616 0.00132 3.56e-03 0.00875
2.1 126.0 0.0547 0.00616 0.00134 3.52e-03 0.00879
2.2 159.0 0.0745 0.00616 0.00136 3.49e-03 0.00882
2.3 200.0 0.0919 0.00616 0.00144 3.33e-03 0.00898
2.4 252.0 0.1070 0.00616 0.00143 3.35e-03 0.00896
2.5 317.0 0.1280 0.00616 0.00148 3.26e-03 0.00905
2.6 399.0 0.1550 0.00616 0.00152 3.17e-03 0.00914
2.7 502.0 0.1770 0.00616 0.00157 3.07e-03 0.00924
2.8 632.0 0.1990 0.00616 0.00157 3.07e-03 0.00924
2.9 796.0 0.2680 0.00616 0.00173 2.77e-03 0.00954
3.0 1000.0 0.2990 0.00616 0.00170 2.82e-03 0.00949
3.1 1260.0 0.3780 0.00616 0.00187 2.49e-03 0.00982
3.2 1590.0 0.4070 0.00616 0.00181 2.61e-03 0.00970
3.3 2000.0 0.5210 0.00515 0.00172 1.78e-03 0.00853
3.4 2520.0 0.5930 0.00271 0.00137 2.84e-05 0.00540
3.5 3170.0 0.6630 0.00202 0.00127 -4.64e-04 0.00451

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.317 0.140 0.0422 0.593
1.4 25.2 0.317 0.182 -0.0389 0.674
1.5 31.7 0.317 0.182 -0.0389 0.674
1.6 39.9 0.317 0.182 -0.0389 0.674
1.7 50.2 0.317 0.182 -0.0389 0.674
1.8 63.2 0.317 0.183 -0.0411 0.676
1.9 79.6 0.317 0.183 -0.0408 0.676
2.0 100.0 0.317 0.178 -0.0310 0.666
2.1 126.0 0.317 0.181 -0.0364 0.671
2.2 159.0 0.317 0.183 -0.0406 0.675
2.3 200.0 0.317 0.194 -0.0619 0.697
2.4 252.0 0.317 0.192 -0.0595 0.694
2.5 317.0 0.317 0.198 -0.0715 0.706
2.6 399.0 0.317 0.204 -0.0833 0.718
2.7 502.0 0.317 0.211 -0.0966 0.731
2.8 632.0 0.317 0.211 -0.0970 0.732
2.9 796.0 0.317 0.232 -0.1370 0.772
3.0 1000.0 0.317 0.228 -0.1300 0.765
3.1 1260.0 0.317 0.251 -0.1740 0.809
3.2 1590.0 0.317 0.243 -0.1580 0.793
3.3 2000.0 0.429 0.220 -0.0022 0.859
3.4 2520.0 0.699 0.159 0.3880 1.010
3.5 3170.0 0.776 0.144 0.4940 1.060

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.00139 0.006290 0.01170
1.4 25.2 0.00598 0.00174 0.002570 0.00939
1.5 31.7 0.00598 0.00174 0.002570 0.00939
1.6 39.9 0.00598 0.00174 0.002570 0.00939
1.7 50.2 0.00605 0.00175 0.002620 0.00949
1.8 63.2 0.00622 0.00184 0.002620 0.00983
1.9 79.6 0.00501 0.00163 0.001820 0.00820
2.0 100.0 0.00474 0.00166 0.001490 0.00798
2.1 126.0 0.00356 0.00159 0.000438 0.00669
2.2 159.0 0.00311 0.00154 0.000102 0.00612
2.3 200.0 0.00277 0.00156 -0.000294 0.00583
2.4 252.0 0.00228 0.00147 -0.000604 0.00516

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.00139 0.006290 0.01170
1.4 25.2 0.263 0.00604 0.00174 0.002630 0.00946
1.5 31.7 0.263 0.00604 0.00174 0.002630 0.00946
1.6 39.9 0.263 0.00604 0.00174 0.002630 0.00946
1.7 50.2 0.269 0.00604 0.00175 0.002610 0.00948
1.8 63.2 0.295 0.00604 0.00184 0.002440 0.00965
1.9 79.6 0.299 0.00501 0.00163 0.001820 0.00820
2.0 100.0 0.325 0.00474 0.00166 0.001490 0.00798
2.1 126.0 0.358 0.00356 0.00159 0.000438 0.00669
2.2 159.0 0.382 0.00311 0.00154 0.000102 0.00612
2.3 200.0 0.436 0.00277 0.00156 -0.000294 0.00583
2.4 252.0 0.452 0.00228 0.00147 -0.000604 0.00516

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-0.959 0.110 0.00522 0.00105 3.17e-03 0.00727
-0.859 0.138 0.00559 0.00124 3.16e-03 0.00802
-0.759 0.174 0.00560 0.00125 3.16e-03 0.00805
-0.659 0.219 0.00563 0.00125 3.18e-03 0.00808
-0.559 0.276 0.00563 0.00125 3.18e-03 0.00808
-0.459 0.348 0.00563 0.00125 3.18e-03 0.00808
-0.359 0.437 0.00565 0.00125 3.19e-03 0.00811
-0.259 0.551 0.00566 0.00126 3.20e-03 0.00812
-0.159 0.693 0.00567 0.00126 3.20e-03 0.00813
-0.059 0.873 0.00545 0.00123 3.03e-03 0.00787
0.041 1.100 0.00573 0.00136 3.06e-03 0.00839
0.141 1.380 0.00590 0.00141 3.14e-03 0.00866
0.241 1.740 0.00591 0.00140 3.16e-03 0.00866
0.341 2.190 0.00615 0.00147 3.26e-03 0.00903
0.441 2.760 0.00590 0.00144 3.07e-03 0.00872
0.541 3.480 0.00596 0.00145 3.13e-03 0.00880
0.641 4.370 0.00607 0.00148 3.16e-03 0.00897
0.741 5.510 0.00582 0.00146 2.97e-03 0.00868
0.841 6.930 0.00538 0.00143 2.58e-03 0.00818
0.941 8.730 0.00563 0.00155 2.59e-03 0.00867
1.040 11.000 0.00587 0.00161 2.71e-03 0.00903
1.140 13.800 0.00536 0.00155 2.32e-03 0.00839
1.240 17.400 0.00575 0.00166 2.51e-03 0.00900
1.340 21.900 0.00532 0.00168 2.03e-03 0.00860
1.440 27.600 0.00561 0.00180 2.09e-03 0.00913
1.540 34.800 0.00526 0.00172 1.89e-03 0.00863
1.640 43.700 0.00654 0.00210 2.43e-03 0.01070
1.740 55.100 0.00661 0.00227 2.16e-03 0.01110
1.840 69.300 0.00752 0.00275 2.12e-03 0.01290
1.940 87.300 0.00740 0.00280 1.92e-03 0.01290
2.040 110.000 0.00574 0.00291 5.07e-05 0.01140

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-0.959 0.110 0.00000 0.00572 0.00105 3.67e-03 0.00777
-0.859 0.138 0.00625 0.00572 0.00124 3.29e-03 0.00816
-0.759 0.174 0.00734 0.00572 0.00125 3.28e-03 0.00817
-0.659 0.219 0.01140 0.00572 0.00125 3.27e-03 0.00818
-0.559 0.276 0.01140 0.00572 0.00125 3.27e-03 0.00818
-0.459 0.348 0.01140 0.00572 0.00125 3.27e-03 0.00818
-0.359 0.437 0.01860 0.00572 0.00125 3.27e-03 0.00818
-0.259 0.551 0.02180 0.00572 0.00126 3.26e-03 0.00819
-0.159 0.693 0.02480 0.00572 0.00126 3.26e-03 0.00819
-0.059 0.873 0.03490 0.00572 0.00123 3.31e-03 0.00814
0.041 1.100 0.09180 0.00572 0.00136 3.06e-03 0.00839
0.141 1.380 0.12000 0.00572 0.00141 2.96e-03 0.00849
0.241 1.740 0.12700 0.00572 0.00140 2.97e-03 0.00848
0.341 2.190 0.17400 0.00572 0.00147 2.84e-03 0.00861
0.441 2.760 0.18200 0.00572 0.00144 2.90e-03 0.00855
0.541 3.480 0.20800 0.00572 0.00145 2.89e-03 0.00856
0.641 4.370 0.21900 0.00572 0.00148 2.82e-03 0.00863
0.741 5.510 0.23100 0.00572 0.00146 2.87e-03 0.00858
0.841 6.930 0.25000 0.00570 0.00143 2.90e-03 0.00850
0.941 8.730 0.27400 0.00570 0.00155 2.66e-03 0.00874
1.040 11.000 0.30700 0.00570 0.00161 2.54e-03 0.00886
1.140 13.800 0.35700 0.00570 0.00155 2.66e-03 0.00873
1.240 17.400 0.39900 0.00570 0.00166 2.45e-03 0.00894
1.340 21.900 0.43100 0.00570 0.00168 2.41e-03 0.00898
1.440 27.600 0.45700 0.00570 0.00180 2.18e-03 0.00922
1.540 34.800 0.51200 0.00570 0.00172 2.33e-03 0.00907
1.640 43.700 0.57000 0.00570 0.00210 1.59e-03 0.00981
1.740 55.100 0.60600 0.00570 0.00227 1.25e-03 0.01020
1.840 69.300 0.66500 0.00570 0.00275 3.00e-04 0.01110
1.940 87.300 0.73500 0.00570 0.00280 2.19e-04 0.01120
2.040 110.000 0.77600 0.00570 0.00291 4.30e-06 0.01140

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-0.959 0.110 0.365 0.137 0.09590 0.634
-0.859 0.138 0.365 0.163 0.04580 0.685
-0.759 0.174 0.365 0.164 0.04430 0.686
-0.659 0.219 0.365 0.164 0.04310 0.687
-0.559 0.276 0.365 0.164 0.04310 0.687
-0.459 0.348 0.365 0.164 0.04310 0.687
-0.359 0.437 0.365 0.165 0.04230 0.688
-0.259 0.551 0.365 0.165 0.04180 0.688
-0.159 0.693 0.365 0.165 0.04140 0.689
-0.059 0.873 0.365 0.162 0.04750 0.683
0.041 1.100 0.365 0.178 0.01560 0.715
0.141 1.380 0.365 0.185 0.00242 0.728
0.241 1.740 0.365 0.184 0.00386 0.726
0.341 2.190 0.365 0.193 -0.01370 0.744
0.441 2.760 0.365 0.190 -0.00638 0.737
0.541 3.480 0.365 0.190 -0.00748 0.738
0.641 4.370 0.365 0.195 -0.01620 0.746
0.741 5.510 0.365 0.191 -0.01010 0.740
0.841 6.930 0.368 0.188 0.00042 0.736
0.941 8.730 0.368 0.204 -0.03090 0.767
1.040 11.000 0.368 0.211 -0.04630 0.782
1.140 13.800 0.368 0.203 -0.03000 0.766
1.240 17.400 0.368 0.217 -0.05780 0.794
1.340 21.900 0.368 0.220 -0.06290 0.799
1.440 27.600 0.368 0.236 -0.09390 0.830
1.540 34.800 0.368 0.225 -0.07360 0.810
1.640 43.700 0.368 0.275 -0.17100 0.908
1.740 55.100 0.368 0.298 -0.21600 0.952
1.840 69.300 0.368 0.361 -0.34000 1.080
1.940 87.300 0.368 0.367 -0.35100 1.090
2.040 110.000 0.368 0.381 -0.37900 1.120

nAb ID50 BA.2

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 3.17e-03 0.00727
1.4 25.2 0.00594 0.00136 3.29e-03 0.00860
1.5 31.7 0.00594 0.00136 3.29e-03 0.00860
1.6 39.9 0.00594 0.00136 3.29e-03 0.00860
1.7 50.2 0.00596 0.00136 3.29e-03 0.00864
1.8 63.2 0.00572 0.00133 3.11e-03 0.00833
1.9 79.6 0.00572 0.00133 3.11e-03 0.00833
2.0 100.0 0.00572 0.00132 3.12e-03 0.00831
2.1 126.0 0.00575 0.00133 3.14e-03 0.00835
2.2 159.0 0.00574 0.00132 3.15e-03 0.00833
2.3 200.0 0.00582 0.00135 3.19e-03 0.00846
2.4 252.0 0.00591 0.00138 3.21e-03 0.00861
2.5 317.0 0.00600 0.00140 3.25e-03 0.00874
2.6 399.0 0.00603 0.00140 3.28e-03 0.00877
2.7 502.0 0.00634 0.00150 3.40e-03 0.00928
2.8 632.0 0.00609 0.00148 3.20e-03 0.00899
2.9 796.0 0.00586 0.00149 2.94e-03 0.00879
3.0 1000.0 0.00573 0.00147 2.85e-03 0.00862
3.1 1260.0 0.00567 0.00149 2.76e-03 0.00858
3.2 1590.0 0.00504 0.00145 2.18e-03 0.00789
3.3 2000.0 0.00466 0.00146 1.80e-03 0.00752
3.4 2520.0 0.00334 0.00130 8.05e-04 0.00588
3.5 3170.0 0.00399 0.00157 9.18e-04 0.00707
3.6 3990.0 0.00286 0.00143 4.31e-05 0.00567
3.7 5020.0 0.00338 0.00191 -3.73e-04 0.00712

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00586 0.00105 0.003810 0.00791
1.4 25.2 0.0405 0.00586 0.00136 0.003200 0.00852
1.5 31.7 0.0405 0.00586 0.00136 0.003200 0.00852
1.6 39.9 0.0405 0.00586 0.00136 0.003200 0.00852
1.7 50.2 0.0415 0.00586 0.00136 0.003190 0.00853
1.8 63.2 0.0423 0.00586 0.00133 0.003250 0.00847
1.9 79.6 0.0423 0.00586 0.00133 0.003250 0.00847
2.0 100.0 0.0453 0.00586 0.00132 0.003260 0.00846
2.1 126.0 0.0504 0.00586 0.00133 0.003260 0.00846
2.2 159.0 0.0537 0.00586 0.00132 0.003270 0.00845
2.3 200.0 0.0670 0.00586 0.00135 0.003220 0.00850
2.4 252.0 0.0759 0.00586 0.00138 0.003160 0.00856
2.5 317.0 0.0956 0.00586 0.00140 0.003120 0.00861
2.6 399.0 0.1050 0.00586 0.00140 0.003120 0.00861
2.7 502.0 0.1240 0.00586 0.00150 0.002920 0.00880
2.8 632.0 0.1280 0.00586 0.00148 0.002970 0.00876
2.9 796.0 0.1650 0.00586 0.00149 0.002930 0.00879
3.0 1000.0 0.2120 0.00573 0.00147 0.002850 0.00862
3.1 1260.0 0.2650 0.00567 0.00149 0.002760 0.00858
3.2 1590.0 0.3330 0.00504 0.00145 0.002180 0.00789
3.3 2000.0 0.3890 0.00466 0.00146 0.001800 0.00752
3.4 2520.0 0.4460 0.00367 0.00130 0.001130 0.00621
3.5 3170.0 0.5660 0.00367 0.00157 0.000594 0.00674
3.6 3990.0 0.6330 0.00312 0.00143 0.000303 0.00593
3.7 5020.0 0.7300 0.00312 0.00191 -0.000633 0.00686

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.350 0.138 0.07890 0.621
1.4 25.2 0.350 0.179 -0.00144 0.702
1.5 31.7 0.350 0.179 -0.00144 0.702
1.6 39.9 0.350 0.179 -0.00144 0.702
1.7 50.2 0.350 0.180 -0.00364 0.704
1.8 63.2 0.350 0.176 0.00506 0.695
1.9 79.6 0.350 0.176 0.00506 0.695
2.0 100.0 0.350 0.175 0.00667 0.693
2.1 126.0 0.350 0.176 0.00572 0.694
2.2 159.0 0.350 0.175 0.00739 0.693
2.3 200.0 0.350 0.178 0.00118 0.699
2.4 252.0 0.350 0.182 -0.00703 0.707
2.5 317.0 0.350 0.185 -0.01290 0.713
2.6 399.0 0.350 0.185 -0.01300 0.713
2.7 502.0 0.350 0.199 -0.03930 0.739
2.8 632.0 0.350 0.195 -0.03270 0.733
2.9 796.0 0.350 0.197 -0.03710 0.737
3.0 1000.0 0.364 0.193 -0.01450 0.743
3.1 1260.0 0.371 0.195 -0.01030 0.752
3.2 1590.0 0.441 0.185 0.07930 0.804
3.3 2000.0 0.483 0.182 0.12600 0.841
3.4 2520.0 0.593 0.155 0.28900 0.897
3.5 3170.0 0.593 0.188 0.22500 0.961
3.6 3990.0 0.654 0.168 0.32400 0.984
3.7 5020.0 0.654 0.224 0.21500 1.090

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.00139 6.29e-03 0.01170
1.4 25.2 0.00577 0.00162 2.59e-03 0.00896
1.5 31.7 0.00577 0.00162 2.59e-03 0.00896
1.6 39.9 0.00577 0.00162 2.59e-03 0.00896
1.7 50.2 0.00589 0.00168 2.60e-03 0.00917
1.8 63.2 0.00554 0.00163 2.35e-03 0.00874
1.9 79.6 0.00487 0.00154 1.86e-03 0.00788
2.0 100.0 0.00414 0.00142 1.36e-03 0.00692
2.1 126.0 0.00325 0.00141 4.97e-04 0.00601
2.2 159.0 0.00244 0.00122 4.41e-05 0.00483
2.3 200.0 0.00207 0.00109 -6.31e-05 0.00421
2.4 252.0 0.00205 0.00102 4.42e-05 0.00405

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.00139 6.29e-03 0.01170
1.4 25.2 0.259 0.00580 0.00162 2.62e-03 0.00899
1.5 31.7 0.259 0.00580 0.00162 2.62e-03 0.00899
1.6 39.9 0.259 0.00580 0.00162 2.62e-03 0.00899
1.7 50.2 0.267 0.00580 0.00168 2.52e-03 0.00908
1.8 63.2 0.272 0.00554 0.00163 2.35e-03 0.00874
1.9 79.6 0.288 0.00487 0.00154 1.86e-03 0.00788
2.0 100.0 0.295 0.00414 0.00142 1.36e-03 0.00692
2.1 126.0 0.347 0.00325 0.00141 4.97e-04 0.00601
2.2 159.0 0.354 0.00244 0.00122 4.40e-05 0.00483
2.3 200.0 0.415 0.00207 0.00109 -6.32e-05 0.00421
2.4 252.0 0.468 0.00205 0.00102 4.42e-05 0.00405

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.5400 0.0290 0.00522 0.00105 0.003170 0.00727
-1.4400 0.0365 0.00580 0.00126 0.003320 0.00827
-1.3400 0.0459 0.00580 0.00126 0.003320 0.00827
-1.2400 0.0578 0.00582 0.00127 0.003340 0.00831
-1.1400 0.0728 0.00586 0.00128 0.003350 0.00836
-1.0400 0.0917 0.00586 0.00128 0.003350 0.00836
-0.9380 0.1150 0.00564 0.00126 0.003170 0.00811
-0.8380 0.1450 0.00564 0.00126 0.003170 0.00811
-0.7380 0.1830 0.00566 0.00126 0.003180 0.00814
-0.6380 0.2300 0.00568 0.00126 0.003200 0.00816
-0.5380 0.2900 0.00569 0.00126 0.003210 0.00817
-0.4380 0.3650 0.00571 0.00127 0.003220 0.00819
-0.3380 0.4590 0.00571 0.00127 0.003220 0.00820
-0.2380 0.5780 0.00571 0.00127 0.003220 0.00820
-0.1380 0.7280 0.00573 0.00127 0.003230 0.00822
-0.0378 0.9170 0.00549 0.00125 0.003050 0.00794
0.0622 1.1500 0.00598 0.00139 0.003260 0.00871
0.1620 1.4500 0.00603 0.00140 0.003280 0.00878
0.2620 1.8300 0.00627 0.00147 0.003400 0.00915
0.3620 2.3000 0.00636 0.00149 0.003440 0.00927
0.4620 2.9000 0.00626 0.00152 0.003280 0.00924
0.5620 3.6500 0.00604 0.00150 0.003110 0.00897
0.6620 4.5900 0.00610 0.00149 0.003170 0.00903
0.7620 5.7800 0.00588 0.00148 0.002980 0.00878
0.8620 7.2800 0.00604 0.00152 0.003060 0.00903
0.9620 9.1700 0.00614 0.00155 0.003110 0.00917
1.0600 11.5000 0.00637 0.00167 0.003100 0.00964
1.1600 14.5000 0.00659 0.00172 0.003220 0.00995
1.2600 18.3000 0.00643 0.00178 0.002940 0.00991
1.3600 23.0000 0.00667 0.00191 0.002930 0.01040
1.4600 29.0000 0.00552 0.00176 0.002080 0.00897
1.5600 36.5000 0.00616 0.00201 0.002210 0.01010
1.6600 45.9000 0.00621 0.00216 0.001980 0.01040
1.7600 57.8000 0.00745 0.00262 0.002310 0.01260
1.8600 72.8000 0.00712 0.00253 0.002170 0.01210
1.9600 91.7000 0.00684 0.00261 0.001720 0.01200
2.0600 115.0000 0.00490 0.00231 0.000368 0.00943
2.1600 145.0000 0.00548 0.00254 0.000500 0.01050
2.2600 183.0000 0.00662 0.00390 -0.001030 0.01430

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.5400 0.0290 0.00000 0.00596 0.00105 0.003910 0.00801
-1.4400 0.0365 0.00300 0.00596 0.00126 0.003490 0.00843
-1.3400 0.0459 0.00300 0.00596 0.00126 0.003490 0.00843
-1.2400 0.0578 0.00601 0.00596 0.00127 0.003470 0.00844
-1.1400 0.0728 0.00901 0.00596 0.00128 0.003450 0.00847
-1.0400 0.0917 0.00901 0.00596 0.00128 0.003450 0.00847
-0.9380 0.1150 0.01030 0.00596 0.00126 0.003490 0.00842
-0.8380 0.1450 0.01030 0.00596 0.00126 0.003490 0.00842
-0.7380 0.1830 0.01330 0.00596 0.00126 0.003480 0.00844
-0.6380 0.2300 0.02130 0.00596 0.00126 0.003480 0.00844
-0.5380 0.2900 0.02730 0.00596 0.00126 0.003480 0.00844
-0.4380 0.3650 0.03330 0.00596 0.00127 0.003470 0.00844
-0.3380 0.4590 0.03410 0.00596 0.00127 0.003470 0.00845
-0.2380 0.5780 0.03410 0.00596 0.00127 0.003470 0.00845
-0.1380 0.7280 0.03790 0.00596 0.00127 0.003460 0.00845
-0.0378 0.9170 0.04260 0.00596 0.00125 0.003520 0.00840
0.0622 1.1500 0.09540 0.00596 0.00139 0.003230 0.00869
0.1620 1.4500 0.10200 0.00596 0.00140 0.003210 0.00871
0.2620 1.8300 0.14700 0.00596 0.00147 0.003080 0.00884
0.3620 2.3000 0.16500 0.00596 0.00149 0.003040 0.00887
0.4620 2.9000 0.18400 0.00596 0.00152 0.002980 0.00893
0.5620 3.6500 0.19700 0.00596 0.00150 0.003030 0.00889
0.6620 4.5900 0.21900 0.00596 0.00149 0.003030 0.00889
0.7620 5.7800 0.22800 0.00596 0.00148 0.003060 0.00886
0.8620 7.2800 0.25900 0.00596 0.00152 0.002980 0.00894
0.9620 9.1700 0.27800 0.00596 0.00155 0.002930 0.00899
1.0600 11.5000 0.32800 0.00596 0.00167 0.002690 0.00922
1.1600 14.5000 0.35700 0.00596 0.00172 0.002590 0.00932
1.2600 18.3000 0.41800 0.00596 0.00178 0.002470 0.00944
1.3600 23.0000 0.45300 0.00596 0.00191 0.002210 0.00970
1.4600 29.0000 0.46000 0.00596 0.00176 0.002510 0.00941
1.5600 36.5000 0.49300 0.00596 0.00201 0.002010 0.00991
1.6600 45.9000 0.52500 0.00596 0.00216 0.001730 0.01020
1.7600 57.8000 0.59400 0.00596 0.00262 0.000814 0.01110
1.8600 72.8000 0.64800 0.00596 0.00253 0.001010 0.01090
1.9600 91.7000 0.68100 0.00596 0.00261 0.000844 0.01110
2.0600 115.0000 0.74000 0.00567 0.00231 0.001140 0.01020
2.1600 145.0000 0.77600 0.00567 0.00254 0.000682 0.01060
2.2600 183.0000 0.85300 0.00567 0.00390 -0.001980 0.01330

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.5400 0.0290 0.339 0.139 0.06680 0.612
-1.4400 0.0365 0.339 0.168 0.01080 0.668
-1.3400 0.0459 0.339 0.168 0.01080 0.668
-1.2400 0.0578 0.339 0.169 0.00873 0.670
-1.1400 0.0728 0.339 0.170 0.00594 0.673
-1.0400 0.0917 0.339 0.170 0.00594 0.673
-0.9380 0.1150 0.339 0.167 0.01160 0.667
-0.8380 0.1450 0.339 0.167 0.01160 0.667
-0.7380 0.1830 0.339 0.168 0.01000 0.668
-0.6380 0.2300 0.339 0.168 0.00986 0.669
-0.5380 0.2900 0.339 0.168 0.00981 0.669
-0.4380 0.3650 0.339 0.169 0.00899 0.670
-0.3380 0.4590 0.339 0.169 0.00869 0.670
-0.2380 0.5780 0.339 0.169 0.00869 0.670
-0.1380 0.7280 0.339 0.169 0.00754 0.671
-0.0378 0.9170 0.339 0.166 0.01470 0.664
0.0622 1.1500 0.339 0.185 -0.02330 0.702
0.1620 1.4500 0.339 0.187 -0.02660 0.705
0.2620 1.8300 0.339 0.195 -0.04330 0.722
0.3620 2.3000 0.339 0.198 -0.04830 0.727
0.4620 2.9000 0.339 0.202 -0.05630 0.735
0.5620 3.6500 0.339 0.199 -0.05050 0.729
0.6620 4.5900 0.339 0.199 -0.04990 0.728
0.7620 5.7800 0.339 0.197 -0.04640 0.725
0.8620 7.2800 0.339 0.202 -0.05730 0.736
0.9620 9.1700 0.339 0.206 -0.06380 0.742
1.0600 11.5000 0.339 0.221 -0.09480 0.773
1.1600 14.5000 0.339 0.228 -0.10800 0.787
1.2600 18.3000 0.339 0.236 -0.12400 0.802
1.3600 23.0000 0.339 0.254 -0.15900 0.837
1.4600 29.0000 0.339 0.234 -0.11900 0.797
1.5600 36.5000 0.339 0.268 -0.18600 0.864
1.6600 45.9000 0.339 0.286 -0.22200 0.901
1.7600 57.8000 0.339 0.349 -0.34500 1.020
1.8600 72.8000 0.339 0.336 -0.31900 0.997
1.9600 91.7000 0.339 0.347 -0.34100 1.020
2.0600 115.0000 0.372 0.303 -0.22200 0.965
2.1600 145.0000 0.372 0.333 -0.28100 1.020
2.2600 183.0000 0.372 0.511 -0.62900 1.370

nAb ID50 BA.4/5

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 0.003170 0.00727
1.4 25.2 0.00579 0.00135 0.003140 0.00844
1.5 31.7 0.00579 0.00135 0.003140 0.00844
1.6 39.9 0.00579 0.00135 0.003140 0.00844
1.7 50.2 0.00582 0.00136 0.003150 0.00850
1.8 63.2 0.00582 0.00136 0.003150 0.00850
1.9 79.6 0.00583 0.00136 0.003170 0.00849
2.0 100.0 0.00531 0.00129 0.002790 0.00784
2.1 126.0 0.00531 0.00129 0.002790 0.00784
2.2 159.0 0.00542 0.00132 0.002830 0.00800
2.3 200.0 0.00577 0.00146 0.002910 0.00863
2.4 252.0 0.00582 0.00147 0.002930 0.00870
2.5 317.0 0.00588 0.00147 0.003000 0.00876
2.6 399.0 0.00542 0.00142 0.002650 0.00820
2.7 502.0 0.00515 0.00135 0.002500 0.00781
2.8 632.0 0.00525 0.00137 0.002560 0.00795
2.9 796.0 0.00491 0.00137 0.002220 0.00759
3.0 1000.0 0.00486 0.00141 0.002090 0.00763
3.1 1260.0 0.00480 0.00146 0.001940 0.00766
3.2 1590.0 0.00440 0.00142 0.001620 0.00719
3.3 2000.0 0.00382 0.00136 0.001160 0.00648
3.4 2520.0 0.00359 0.00150 0.000653 0.00652
3.5 3170.0 0.00380 0.00172 0.000436 0.00716
3.6 3990.0 0.00406 0.00219 -0.000235 0.00836

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00572 0.00105 0.003670 0.00777
1.4 25.2 0.0579 0.00572 0.00135 0.003070 0.00837
1.5 31.7 0.0579 0.00572 0.00135 0.003070 0.00837
1.6 39.9 0.0579 0.00572 0.00135 0.003070 0.00837
1.7 50.2 0.0609 0.00572 0.00136 0.003050 0.00840
1.8 63.2 0.0612 0.00572 0.00136 0.003050 0.00840
1.9 79.6 0.0672 0.00572 0.00136 0.003060 0.00838
2.0 100.0 0.0712 0.00558 0.00129 0.003060 0.00810
2.1 126.0 0.0712 0.00558 0.00129 0.003060 0.00810
2.2 159.0 0.0866 0.00558 0.00132 0.002990 0.00817
2.3 200.0 0.1070 0.00558 0.00146 0.002720 0.00844
2.4 252.0 0.1150 0.00558 0.00147 0.002690 0.00847
2.5 317.0 0.1370 0.00558 0.00147 0.002700 0.00846
2.6 399.0 0.1550 0.00542 0.00142 0.002650 0.00820
2.7 502.0 0.1860 0.00520 0.00135 0.002550 0.00786
2.8 632.0 0.2150 0.00520 0.00137 0.002510 0.00790
2.9 796.0 0.2490 0.00491 0.00137 0.002220 0.00759
3.0 1000.0 0.2970 0.00486 0.00141 0.002090 0.00763
3.1 1260.0 0.3600 0.00480 0.00146 0.001940 0.00766
3.2 1590.0 0.4260 0.00440 0.00142 0.001620 0.00719
3.3 2000.0 0.4670 0.00382 0.00136 0.001160 0.00648
3.4 2520.0 0.5750 0.00382 0.00150 0.000883 0.00675
3.5 3170.0 0.6670 0.00382 0.00172 0.000454 0.00718
3.6 3990.0 0.7640 0.00382 0.00219 -0.000483 0.00812

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.365 0.137 0.09620 0.635
1.4 25.2 0.365 0.178 0.01750 0.713
1.5 31.7 0.365 0.178 0.01750 0.713
1.6 39.9 0.365 0.178 0.01750 0.713
1.7 50.2 0.365 0.179 0.01410 0.717
1.8 63.2 0.365 0.179 0.01410 0.717
1.9 79.6 0.365 0.178 0.01620 0.715
2.0 100.0 0.381 0.168 0.05200 0.710
2.1 126.0 0.381 0.168 0.05200 0.710
2.2 159.0 0.381 0.172 0.04400 0.718
2.3 200.0 0.381 0.190 0.00806 0.754
2.4 252.0 0.381 0.192 0.00491 0.757
2.5 317.0 0.381 0.192 0.00556 0.757
2.6 399.0 0.398 0.184 0.03880 0.758
2.7 502.0 0.423 0.173 0.08310 0.763
2.8 632.0 0.423 0.176 0.07810 0.768
2.9 796.0 0.456 0.173 0.11700 0.795
3.0 1000.0 0.461 0.178 0.11200 0.810
3.1 1260.0 0.467 0.183 0.10800 0.827
3.2 1590.0 0.512 0.175 0.16800 0.855
3.3 2000.0 0.577 0.164 0.25600 0.897
3.4 2520.0 0.577 0.180 0.22300 0.930
3.5 3170.0 0.577 0.207 0.17200 0.982
3.6 3990.0 0.577 0.264 0.05890 1.090

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.001390 0.006290 0.01170
1.4 25.2 0.00425 0.001370 0.001550 0.00694
1.5 31.7 0.00425 0.001370 0.001550 0.00694
1.6 39.9 0.00425 0.001370 0.001550 0.00694
1.7 50.2 0.00453 0.001490 0.001620 0.00744
1.8 63.2 0.00451 0.001420 0.001720 0.00729
1.9 79.6 0.00475 0.001520 0.001780 0.00773
2.0 100.0 0.00361 0.001350 0.000958 0.00625
2.1 126.0 0.00233 0.001070 0.000225 0.00443
2.2 159.0 0.00195 0.000963 0.000058 0.00383
2.3 200.0 0.00152 0.000867 -0.000183 0.00322

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.001390 6.29e-03 0.01170
1.4 25.2 0.278 0.00442 0.001370 1.72e-03 0.00711
1.5 31.7 0.278 0.00442 0.001370 1.72e-03 0.00711
1.6 39.9 0.278 0.00442 0.001370 1.72e-03 0.00711
1.7 50.2 0.307 0.00442 0.001490 1.50e-03 0.00733
1.8 63.2 0.335 0.00442 0.001420 1.63e-03 0.00720
1.9 79.6 0.360 0.00442 0.001520 1.44e-03 0.00739
2.0 100.0 0.385 0.00361 0.001350 9.58e-04 0.00625
2.1 126.0 0.404 0.00233 0.001070 2.25e-04 0.00443
2.2 159.0 0.444 0.00195 0.000963 5.79e-05 0.00383
2.3 200.0 0.462 0.00152 0.000867 -1.84e-04 0.00322

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3500 0.0443 0.00522 0.00105 0.003170 0.00727
-1.2500 0.0558 0.00580 0.00126 0.003320 0.00827
-1.1500 0.0703 0.00583 0.00127 0.003340 0.00832
-1.0500 0.0885 0.00586 0.00128 0.003360 0.00836
-0.9530 0.1110 0.00588 0.00128 0.003360 0.00839
-0.8530 0.1400 0.00588 0.00128 0.003360 0.00839
-0.7530 0.1770 0.00590 0.00129 0.003370 0.00842
-0.6530 0.2220 0.00592 0.00129 0.003380 0.00846
-0.5530 0.2800 0.00593 0.00129 0.003400 0.00846
-0.4530 0.3520 0.00600 0.00131 0.003430 0.00857
-0.3530 0.4430 0.00600 0.00131 0.003430 0.00857
-0.2530 0.5580 0.00577 0.00128 0.003250 0.00829
-0.1530 0.7030 0.00580 0.00129 0.003270 0.00833
-0.0531 0.8850 0.00580 0.00129 0.003270 0.00833
0.0469 1.1100 0.00600 0.00139 0.003280 0.00872
0.1470 1.4000 0.00605 0.00140 0.003310 0.00879
0.2470 1.7700 0.00612 0.00141 0.003350 0.00889
0.3470 2.2200 0.00602 0.00143 0.003210 0.00883
0.4470 2.8000 0.00595 0.00147 0.003060 0.00884
0.5470 3.5200 0.00609 0.00152 0.003120 0.00907
0.6470 4.4300 0.00587 0.00149 0.002950 0.00879
0.7470 5.5800 0.00531 0.00141 0.002560 0.00807
0.8470 7.0300 0.00472 0.00131 0.002150 0.00730
0.9470 8.8500 0.00485 0.00135 0.002200 0.00750
1.0500 11.1000 0.00516 0.00155 0.002120 0.00821
1.1500 14.0000 0.00575 0.00172 0.002370 0.00913
1.2500 17.7000 0.00544 0.00168 0.002150 0.00872
1.3500 22.2000 0.00534 0.00176 0.001890 0.00878
1.4500 28.0000 0.00526 0.00174 0.001860 0.00866
1.5500 35.2000 0.00575 0.00192 0.001990 0.00950
1.6500 44.3000 0.00604 0.00215 0.001830 0.01020
1.7500 55.8000 0.00728 0.00255 0.002280 0.01230
1.8500 70.3000 0.00779 0.00291 0.002080 0.01350
1.9500 88.5000 0.00593 0.00253 0.000958 0.01090
2.0500 111.0000 0.00676 0.00295 0.000979 0.01250
2.1500 140.0000 0.00707 0.00340 0.000417 0.01370

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.3500 0.0443 0.00000 0.00589 0.00105 0.003840 0.00794
-1.2500 0.0558 0.00300 0.00589 0.00126 0.003420 0.00836
-1.1500 0.0703 0.00601 0.00589 0.00127 0.003400 0.00838
-1.0500 0.0885 0.01200 0.00589 0.00128 0.003390 0.00839
-0.9530 0.1110 0.01310 0.00589 0.00128 0.003370 0.00840
-0.8530 0.1400 0.01310 0.00589 0.00128 0.003370 0.00840
-0.7530 0.1770 0.01610 0.00589 0.00129 0.003360 0.00841
-0.6530 0.2220 0.01720 0.00589 0.00129 0.003350 0.00843
-0.5530 0.2800 0.02410 0.00589 0.00129 0.003350 0.00842
-0.4530 0.3520 0.03190 0.00589 0.00131 0.003320 0.00846
-0.3530 0.4430 0.03190 0.00589 0.00131 0.003320 0.00846
-0.2530 0.5580 0.03870 0.00589 0.00128 0.003370 0.00841
-0.1530 0.7030 0.04860 0.00589 0.00129 0.003360 0.00842
-0.0531 0.8850 0.04860 0.00589 0.00129 0.003360 0.00842
0.0469 1.1100 0.10700 0.00589 0.00139 0.003160 0.00861
0.1470 1.4000 0.11800 0.00589 0.00140 0.003150 0.00863
0.2470 1.7700 0.13500 0.00589 0.00141 0.003120 0.00865
0.3470 2.2200 0.16400 0.00589 0.00143 0.003080 0.00869
0.4470 2.8000 0.18900 0.00589 0.00147 0.003000 0.00878
0.5470 3.5200 0.20900 0.00589 0.00152 0.002910 0.00887
0.6470 4.4300 0.23700 0.00587 0.00149 0.002950 0.00879
0.7470 5.5800 0.26000 0.00548 0.00141 0.002720 0.00824
0.8470 7.0300 0.27700 0.00548 0.00131 0.002910 0.00805
0.9470 8.8500 0.29200 0.00548 0.00135 0.002830 0.00813
1.0500 11.1000 0.34900 0.00548 0.00155 0.002430 0.00853
1.1500 14.0000 0.38000 0.00548 0.00172 0.002100 0.00886
1.2500 17.7000 0.39400 0.00548 0.00168 0.002190 0.00877
1.3500 22.2000 0.43600 0.00548 0.00176 0.002040 0.00892
1.4500 28.0000 0.50400 0.00548 0.00174 0.002080 0.00888
1.5500 35.2000 0.55400 0.00548 0.00192 0.001730 0.00923
1.6500 44.3000 0.60100 0.00548 0.00215 0.001270 0.00969
1.7500 55.8000 0.63500 0.00548 0.00255 0.000483 0.01050
1.8500 70.3000 0.68000 0.00548 0.00291 -0.000233 0.01120
1.9500 88.5000 0.73800 0.00548 0.00253 0.000512 0.01040
2.0500 111.0000 0.78100 0.00548 0.00295 -0.000301 0.01130
2.1500 140.0000 0.83100 0.00548 0.00340 -0.001180 0.01210

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.3500 0.0443 0.347 0.139 0.0757 0.619
-1.2500 0.0558 0.347 0.167 0.0198 0.674
-1.1500 0.0703 0.347 0.168 0.0172 0.677
-1.0500 0.0885 0.347 0.169 0.0158 0.678
-0.9530 0.1110 0.347 0.170 0.0144 0.680
-0.8530 0.1400 0.347 0.170 0.0144 0.680
-0.7530 0.1770 0.347 0.171 0.0127 0.682
-0.6530 0.2220 0.347 0.171 0.0110 0.683
-0.5530 0.2800 0.347 0.171 0.0117 0.683
-0.4530 0.3520 0.347 0.174 0.0066 0.688
-0.3530 0.4430 0.347 0.174 0.0066 0.688
-0.2530 0.5580 0.347 0.170 0.0136 0.681
-0.1530 0.7030 0.347 0.171 0.0120 0.682
-0.0531 0.8850 0.347 0.171 0.0120 0.682
0.0469 1.1100 0.347 0.184 -0.0135 0.708
0.1470 1.4000 0.347 0.185 -0.0156 0.710
0.2470 1.7700 0.347 0.187 -0.0192 0.713
0.3470 2.2200 0.347 0.190 -0.0246 0.719
0.4470 2.8000 0.347 0.195 -0.0356 0.730
0.5470 3.5200 0.347 0.201 -0.0473 0.742
0.6470 4.4300 0.349 0.197 -0.0368 0.736
0.7470 5.5800 0.392 0.182 0.0346 0.750
0.8470 7.0300 0.392 0.170 0.0584 0.726
0.9470 8.8500 0.392 0.176 0.0482 0.736
1.0500 11.1000 0.392 0.202 -0.0030 0.788
1.1500 14.0000 0.392 0.224 -0.0462 0.831
1.2500 17.7000 0.392 0.218 -0.0342 0.819
1.3500 22.2000 0.392 0.228 -0.0544 0.839
1.4500 28.0000 0.392 0.225 -0.0490 0.834
1.5500 35.2000 0.392 0.249 -0.0948 0.879
1.6500 44.3000 0.392 0.279 -0.1540 0.939
1.7500 55.8000 0.392 0.331 -0.2560 1.040
1.8500 70.3000 0.392 0.378 -0.3490 1.130
1.9500 88.5000 0.392 0.329 -0.2520 1.040
2.0500 111.0000 0.392 0.383 -0.3580 1.140
2.1500 140.0000 0.392 0.441 -0.4720 1.260

nAb ID50 Breadth Score

Vaccine

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00522 0.00105 0.003170 0.00727
1.4 25.2 0.00596 0.00132 0.003370 0.00854
1.5 31.7 0.00596 0.00132 0.003370 0.00855
1.6 39.9 0.00597 0.00131 0.003400 0.00853
1.7 50.2 0.00606 0.00134 0.003430 0.00870
1.8 63.2 0.00617 0.00139 0.003450 0.00890
1.9 79.6 0.00593 0.00136 0.003270 0.00860
2.0 100.0 0.00595 0.00137 0.003280 0.00863
2.1 126.0 0.00571 0.00134 0.003100 0.00833
2.2 159.0 0.00571 0.00132 0.003120 0.00831
2.3 200.0 0.00572 0.00132 0.003130 0.00831
2.4 252.0 0.00580 0.00135 0.003160 0.00844
2.5 317.0 0.00587 0.00135 0.003220 0.00852
2.6 399.0 0.00590 0.00136 0.003230 0.00858
2.7 502.0 0.00601 0.00140 0.003270 0.00875
2.8 632.0 0.00609 0.00142 0.003300 0.00888
2.9 796.0 0.00590 0.00146 0.003050 0.00876
3.0 1000.0 0.00593 0.00146 0.003070 0.00879
3.1 1260.0 0.00569 0.00143 0.002900 0.00849
3.2 1590.0 0.00559 0.00144 0.002770 0.00842
3.3 2000.0 0.00561 0.00148 0.002720 0.00851
3.4 2520.0 0.00463 0.00140 0.001900 0.00737
3.5 3170.0 0.00421 0.00137 0.001530 0.00689
3.6 3990.0 0.00418 0.00141 0.001410 0.00694
3.7 5020.0 0.00355 0.00146 0.000700 0.00641
3.8 6320.0 0.00266 0.00144 -0.000171 0.00549

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.0000 0.00590 0.00105 0.003850 0.00795
1.4 25.2 0.0122 0.00590 0.00132 0.003320 0.00848
1.5 31.7 0.0127 0.00590 0.00132 0.003320 0.00849
1.6 39.9 0.0157 0.00590 0.00131 0.003340 0.00846
1.7 50.2 0.0250 0.00590 0.00134 0.003270 0.00854
1.8 63.2 0.0358 0.00590 0.00139 0.003180 0.00863
1.9 79.6 0.0366 0.00590 0.00136 0.003240 0.00857
2.0 100.0 0.0381 0.00590 0.00137 0.003220 0.00858
2.1 126.0 0.0384 0.00586 0.00134 0.003250 0.00848
2.2 159.0 0.0444 0.00586 0.00132 0.003270 0.00846
2.3 200.0 0.0485 0.00586 0.00132 0.003270 0.00845
2.4 252.0 0.0591 0.00586 0.00135 0.003220 0.00851
2.5 317.0 0.0796 0.00586 0.00135 0.003210 0.00852
2.6 399.0 0.0836 0.00586 0.00136 0.003190 0.00854
2.7 502.0 0.1010 0.00586 0.00140 0.003120 0.00860
2.8 632.0 0.1150 0.00586 0.00142 0.003080 0.00865
2.9 796.0 0.1480 0.00586 0.00146 0.003010 0.00872
3.0 1000.0 0.1530 0.00586 0.00146 0.003000 0.00872
3.1 1260.0 0.1600 0.00569 0.00143 0.002900 0.00849
3.2 1590.0 0.1920 0.00560 0.00144 0.002780 0.00843
3.3 2000.0 0.2470 0.00560 0.00148 0.002710 0.00849
3.4 2520.0 0.3050 0.00463 0.00140 0.001900 0.00737
3.5 3170.0 0.3660 0.00421 0.00137 0.001530 0.00689
3.6 3990.0 0.4640 0.00418 0.00141 0.001410 0.00694
3.7 5020.0 0.5600 0.00355 0.00146 0.000700 0.00641
3.8 6320.0 0.6650 0.00266 0.00144 -0.000171 0.00549

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.346 0.139 0.073800 0.617
1.4 25.2 0.346 0.175 0.003240 0.688
1.5 31.7 0.346 0.175 0.002810 0.688
1.6 39.9 0.346 0.173 0.006070 0.685
1.7 50.2 0.346 0.178 -0.003640 0.695
1.8 63.2 0.346 0.184 -0.015900 0.707
1.9 79.6 0.346 0.180 -0.007740 0.699
2.0 100.0 0.346 0.181 -0.009530 0.701
2.1 126.0 0.350 0.177 0.003560 0.696
2.2 159.0 0.350 0.175 0.006870 0.693
2.3 200.0 0.350 0.175 0.007390 0.692
2.4 252.0 0.350 0.178 0.000296 0.699
2.5 317.0 0.350 0.179 -0.001140 0.701
2.6 399.0 0.350 0.180 -0.003910 0.703
2.7 502.0 0.350 0.185 -0.012800 0.712
2.8 632.0 0.350 0.188 -0.018600 0.718
2.9 796.0 0.350 0.193 -0.028200 0.728
3.0 1000.0 0.350 0.193 -0.028600 0.728
3.1 1260.0 0.369 0.187 0.001840 0.735
3.2 1590.0 0.379 0.188 0.009830 0.748
3.3 2000.0 0.379 0.193 0.001140 0.756
3.4 2520.0 0.486 0.174 0.145000 0.827
3.5 3170.0 0.533 0.167 0.205000 0.861
3.6 3990.0 0.537 0.172 0.199000 0.875
3.7 5020.0 0.606 0.174 0.266000 0.946
3.8 6320.0 0.705 0.167 0.378000 1.030

Placebo

Not monotone

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
1.3 20.0 0.00902 0.001390 0.006290 0.01170
1.4 25.2 0.00858 0.001820 0.005010 0.01210
1.5 31.7 0.00848 0.001850 0.004840 0.01210
1.6 39.9 0.00683 0.001680 0.003530 0.01010
1.7 50.2 0.00521 0.001500 0.002260 0.00815
1.8 63.2 0.00470 0.001470 0.001830 0.00758
1.9 79.6 0.00445 0.001390 0.001720 0.00718
2.0 100.0 0.00405 0.001330 0.001450 0.00666
2.1 126.0 0.00425 0.001420 0.001470 0.00703
2.2 159.0 0.00395 0.001390 0.001220 0.00668
2.3 200.0 0.00355 0.001320 0.000956 0.00614
2.4 252.0 0.00307 0.001350 0.000429 0.00571
2.5 317.0 0.00262 0.001260 0.000159 0.00508
2.6 399.0 0.00156 0.000900 -0.000208 0.00332
2.7 502.0 0.00163 0.000944 -0.000217 0.00348

Monotone

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
1.3 20.0 0.000 0.00902 0.001390 0.006290 0.01170
1.4 25.2 0.105 0.00858 0.001820 0.005010 0.01210
1.5 31.7 0.157 0.00848 0.001850 0.004840 0.01210
1.6 39.9 0.184 0.00683 0.001680 0.003530 0.01010
1.7 50.2 0.254 0.00521 0.001500 0.002260 0.00815
1.8 63.2 0.269 0.00470 0.001470 0.001830 0.00758
1.9 79.6 0.311 0.00445 0.001390 0.001720 0.00718
2.0 100.0 0.327 0.00415 0.001330 0.001550 0.00676
2.1 126.0 0.371 0.00415 0.001420 0.001370 0.00693
2.2 159.0 0.383 0.00395 0.001390 0.001220 0.00668
2.3 200.0 0.386 0.00355 0.001320 0.000956 0.00614
2.4 252.0 0.424 0.00307 0.001350 0.000429 0.00571
2.5 317.0 0.439 0.00262 0.001260 0.000159 0.00508
2.6 399.0 0.476 0.00159 0.000900 -0.000169 0.00336
2.7 502.0 0.507 0.00159 0.000944 -0.000256 0.00344

Vaccine (change)

Unscaled (not monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0200 0.0955 0.00522 0.00105 0.00317 0.00727
-0.9200 0.1200 0.00582 0.00127 0.00334 0.00830
-0.8200 0.1510 0.00586 0.00128 0.00335 0.00837
-0.7200 0.1900 0.00589 0.00128 0.00337 0.00840
-0.6200 0.2400 0.00592 0.00129 0.00338 0.00846
-0.5200 0.3020 0.00593 0.00129 0.00340 0.00846
-0.4200 0.3800 0.00594 0.00129 0.00340 0.00847
-0.3200 0.4780 0.00594 0.00129 0.00340 0.00848
-0.2200 0.6020 0.00595 0.00130 0.00341 0.00849
-0.1200 0.7580 0.00596 0.00130 0.00341 0.00850
-0.0202 0.9550 0.00602 0.00132 0.00345 0.00860
0.0798 1.2000 0.00608 0.00137 0.00340 0.00876
0.1800 1.5100 0.00589 0.00135 0.00325 0.00853
0.2800 1.9000 0.00600 0.00138 0.00330 0.00870
0.3800 2.4000 0.00630 0.00147 0.00343 0.00918
0.4800 3.0200 0.00623 0.00151 0.00327 0.00918
0.5800 3.8000 0.00602 0.00148 0.00311 0.00893
0.6800 4.7800 0.00580 0.00145 0.00295 0.00865
0.7800 6.0200 0.00555 0.00142 0.00276 0.00834
0.8800 7.5800 0.00563 0.00145 0.00280 0.00846
0.9800 9.5500 0.00603 0.00157 0.00296 0.00910
1.0800 12.0000 0.00558 0.00153 0.00259 0.00857
1.1800 15.1000 0.00594 0.00162 0.00276 0.00913
1.2800 19.0000 0.00526 0.00158 0.00217 0.00836
1.3800 24.0000 0.00543 0.00165 0.00221 0.00866
1.4800 30.2000 0.00560 0.00178 0.00211 0.00909
1.5800 38.0000 0.00585 0.00189 0.00215 0.00956
1.6800 47.8000 0.00601 0.00205 0.00200 0.01000
1.7800 60.2000 0.00713 0.00239 0.00245 0.01180
1.8800 75.8000 0.00745 0.00253 0.00248 0.01240
1.9800 95.5000 0.00673 0.00254 0.00175 0.01170
2.0800 120.0000 0.00575 0.00249 0.00087 0.01060
2.1800 151.0000 0.00342 0.00240 -0.00127 0.00812

Unscaled (monotone)

Threshold (log10) Threshold RCDF Estimate SE Lower CI Upper CI
-1.0200 0.0955 0.00000 0.00593 0.00105 0.003890 0.00798
-0.9200 0.1200 0.00601 0.00593 0.00127 0.003450 0.00842
-0.8200 0.1510 0.01010 0.00593 0.00128 0.003430 0.00844
-0.7200 0.1900 0.01420 0.00593 0.00128 0.003420 0.00845
-0.6200 0.2400 0.01720 0.00593 0.00129 0.003400 0.00847
-0.5200 0.3020 0.02410 0.00593 0.00129 0.003400 0.00847
-0.4200 0.3800 0.02710 0.00593 0.00129 0.003400 0.00847
-0.3200 0.4780 0.02740 0.00593 0.00129 0.003400 0.00847
-0.2200 0.6020 0.03040 0.00593 0.00130 0.003390 0.00848
-0.1200 0.7580 0.03360 0.00593 0.00130 0.003390 0.00848
-0.0202 0.9550 0.04650 0.00593 0.00132 0.003360 0.00851
0.0798 1.2000 0.07080 0.00593 0.00137 0.003250 0.00862
0.1800 1.5100 0.08850 0.00593 0.00135 0.003300 0.00857
0.2800 1.9000 0.11300 0.00593 0.00138 0.003240 0.00863
0.3800 2.4000 0.15700 0.00593 0.00147 0.003060 0.00881
0.4800 3.0200 0.17600 0.00593 0.00151 0.002980 0.00889
0.5800 3.8000 0.19100 0.00593 0.00148 0.003030 0.00884
0.6800 4.7800 0.21700 0.00590 0.00145 0.003050 0.00875
0.7800 6.0200 0.23400 0.00590 0.00142 0.003110 0.00868
0.8800 7.5800 0.24900 0.00590 0.00145 0.003060 0.00873
0.9800 9.5500 0.27600 0.00590 0.00157 0.002830 0.00897
1.0800 12.0000 0.31500 0.00590 0.00153 0.002900 0.00889
1.1800 15.1000 0.34800 0.00590 0.00162 0.002710 0.00908
1.2800 19.0000 0.38100 0.00590 0.00158 0.002800 0.00899
1.3800 24.0000 0.40500 0.00590 0.00165 0.002670 0.00912
1.4800 30.2000 0.46200 0.00590 0.00178 0.002410 0.00938
1.5800 38.0000 0.49600 0.00590 0.00189 0.002190 0.00960
1.6800 47.8000 0.55300 0.00590 0.00205 0.001890 0.00991
1.7800 60.2000 0.61100 0.00590 0.00239 0.001220 0.01060
1.8800 75.8000 0.63500 0.00590 0.00253 0.000934 0.01090
1.9800 95.5000 0.66500 0.00590 0.00254 0.000920 0.01090
2.0800 120.0000 0.69400 0.00575 0.00249 0.000870 0.01060
2.1800 151.0000 0.80000 0.00342 0.00240 -0.001270 0.00812

VE scale (1 minus risk / placebo risk) (monotone)

Threshold (log10) Threshold Estimate SE Lower CI Upper CI
-1.0200 0.0955 0.342 0.139 0.069700 0.614
-0.9200 0.1200 0.342 0.168 0.012400 0.671
-0.8200 0.1510 0.342 0.170 0.008730 0.675
-0.7200 0.1900 0.342 0.170 0.007810 0.676
-0.6200 0.2400 0.342 0.172 0.004890 0.679
-0.5200 0.3020 0.342 0.172 0.005410 0.678
-0.4200 0.3800 0.342 0.172 0.004990 0.679
-0.3200 0.4780 0.342 0.172 0.004890 0.679
-0.2200 0.6020 0.342 0.172 0.004510 0.679
-0.1200 0.7580 0.342 0.172 0.004000 0.680
-0.0202 0.9550 0.342 0.175 -0.000417 0.684
0.0798 1.2000 0.342 0.182 -0.014100 0.698
0.1800 1.5100 0.342 0.179 -0.008640 0.692
0.2800 1.9000 0.342 0.183 -0.016200 0.700
0.3800 2.4000 0.342 0.195 -0.040000 0.724
0.4800 3.0200 0.342 0.200 -0.050200 0.734
0.5800 3.8000 0.342 0.197 -0.044400 0.728
0.6800 4.7800 0.346 0.193 -0.031600 0.724
0.7800 6.0200 0.346 0.188 -0.023300 0.715
0.8800 7.5800 0.346 0.192 -0.029300 0.721
0.9800 9.5500 0.346 0.207 -0.060600 0.753
1.0800 12.0000 0.346 0.202 -0.050700 0.743
1.1800 15.1000 0.346 0.215 -0.075600 0.768
1.2800 19.0000 0.346 0.209 -0.064500 0.757
1.3800 24.0000 0.346 0.218 -0.081300 0.773
1.4800 30.2000 0.346 0.236 -0.116000 0.808
1.5800 38.0000 0.346 0.251 -0.145000 0.837
1.6800 47.8000 0.346 0.271 -0.185000 0.877
1.7800 60.2000 0.346 0.316 -0.274000 0.966
1.8800 75.8000 0.346 0.336 -0.312000 1.000
1.9800 95.5000 0.346 0.336 -0.313000 1.010
2.0800 120.0000 0.362 0.327 -0.279000 1.000
2.1800 151.0000 0.620 0.284 0.063300 1.180